Book 4 (Fixed income, derivatives, real estate)

Accrued Interest =

(Days since last coupon payment/Days between coupon payment) * Coupon amount

LIBOR - OIS Spread

(OIS Rate reflects the Overnight indexed swap rate which is the federal funds rate and includes minimum credit risk) LIBOR - OIS spread is a good indicator of credit risk and overall wellbeing of the banking system Low LIBOR - OIS Spread indicated high market liquidity High LIBOR - OIS Spread indicated Low Market Liquidity

Key Rate Duration

(Partial Duration) Captures the interest rate sensitivity of a bond to changes in yields (Par rates) of a specefic benchmark maturity. Key Rate duration is used to identify the interest rate risk from changes in the shape of the yield curve (Shaping risk)

Sinking Funds Bonds

(Sinkers) which require the issuer to set aside funds periodically to retire the bond (sinking fund). This provision reduces the credit risk of the bond. Sinkers typically have several related issuer options

Combinations of interest rate options can be used to replicate other contract; such as:

1) A long interest call and a short interest rate put (with X = Current FRA rate) can be used to replicate a long FRA 2) Similarly, the the exercise rate = current FRA rate, A short interest rate call and a long intrerest rate out can be combined to replicate a short FRA position 3) A series of interes rate call options with different maturities and the same exercise price can be combined to form an interest rate cap. A floating rate loan be hedged using a long interest rate cap 4) Similarly an interest rate floor is a portfolio of interest rate put options, and each of these puts is known as a flooret. floors can be used to hedge a long position in a floating rate bond 5) If the exercise rate on a cap and floor is the same, a long cap and a short floor can be used to replicate a payer swap 6) Similarly a short cap and a long floor can replicate a receiver swap 7) If the exercise rate on a floor and a cap are set equal to a market swap fixed rate, the value of the cap will equal to the value of the floor

Time conventions for calculations

1) All LIBOR based, FRA's, Swaps. Caps, Floors: 360-day convention, (r*(day/360)) 2) Equities, bonds, currencies, stock options: 365 days, (1+r)^(days/365) 3)Equity Indexes: continuously compounded, raise e^(r* Days/365)

Ways to determine NAV

1) At cost, adjusting for subsequent financing and devaluation 2) At the minimum of cost or market value 3) By revaluing the portfolio company anytime there is new financing 4)At Cost, with no adjustment until exit 5) By using a discount factor for restricted securities 6) less frequently, by applying illiquidity discounts to values based on those of comparable publicly traded companies

Components of Credit Analysis:

1) Collateral Pool: Credit analysis of structured securitized debt begins with the collateral pool. Homogeneity of a pool refers to similarity of assets within the collateral pool. Granularity refers to the transparency of assets within the pool. A highly granular pool would have hundreds of clearly defined loans, allowing for summary statistics to be used 2) Servicer Quality: is important to evaluate the ability of the servicer to manage the origination and servicing of the collateral pool. After origination, investors in secured debt face the operational and counterparty risks in a collateral pool. One Key Structural element is credit enhancement, which may be internal or external. 3) Structure: Determines the trenching or other management of credit and other risks in a collateral pool. One key structural element is credit enhancement, which may be internal or external

Factors driving the Development of electronic trading systems are:

1) Cost 2) accuracy 3)Audit trails 4) Fraud prevention 5) Continuous market

3 different approaches to valuing real estate

1) Cost approach: is that a buyer would not pay more for a property than it would cost to purchase land and construct a comparable building. Under the cost approach, value is derived by adding the value of the land to the current replacement costs of a new building, less adjustments for estimated depreciation and obsolescence: Cost approach is best used when the entity is newly constructed 2) Sales Comparison Approach: Is that a buyer would pay no more for a property than others are paying for similar properties. The sales prices of similar properties are adjusted for differences within subject property. The sales comparison approach is good when there are a number of similar properties to the subject that have recently sold 3) Income Approach: Is the value based on the expected rate of return required by a buyer to invest in the subject property. With the income approach, value is equal to the present value of the subjects future cash flows. the income approach is most useful in commercial real estate transactions

Determinants of Term structure of Credit spreads

1) Credit Quality: Is an important factor driving terms structure; AAA terms tend to be flat or slightly upward sloping. Lower-rated sectors tend to have steeper spread curves 2) Financial Conditions affect the credit spread curve. Spreads Narrow during economic Expansions and widen during cyclical downturns. During boom times, benchmark yields tend to be higher while credit spreads tend to be more narrow 3) Market Demand and supply; influence the shape of the spread curve. Recall that a credit spread includes a premium for lack of liquidity. hence, less liquid maturities would show higher spreads (Even if the expectations for that time period are stable). Due to low liquidity in most corporate issues, the credit curves are most heavily influenced by more heavily traded bonds. Because newly issued bonds are generally more liquid, when an issuer refinances a near dated bond with a longer term bond, the spread may appear to narrow for the longer maturity (possibly leading to an inverted credit spread curve) 4) Equity Market Volatility: Company value models (Structural models) employ a company's stock price volatility and balance sheet structure in determining the probabilities of default. Increases in equity volatility therefore tend to widen spreads and influence the shape of the credit spread curve

Income approach for Real Estate has 2 methods

1) Direct Capitalization method 2) DCF

Six methodologies to valuing private equity portfolio companies:

1) Discount Cash Flow method (DCF) is most appropriate for companies with a significant operating history because it requires an estimate of cash flows 2) A relative value or market approach: applies a price multiple, such as P/E, against the company's earnings to get an estimate of the company's valuation. This approach uses predictable cash flows and a significant history 3) Real option analysis 4) this approach uses Replacement Cost of the business. It is generally not applicable to mature companies whose historical value added would be hard to estimate 5) Venture capital and LBO methods

Sources of tracking error for an ETF include:

1) Fees and expense 2) Sampling and optimization 3) Depository receipts 4) Index changes 5) regulatory and tax requirements 6) Fund accounting practices 7) Asset Manager Operations

Types of exit routes for a Private Equity firm

1) IPO 2) Secondary market sale 3) MBO 4) Liquidation

Generalizations can be made about key rates:

1) If an option free bond is trading at par, the bonds maturity matched rate is the only rate that affects the bonds value 2) For an option free bond, not trading at par, the maturity matched rate is still the most important rate 3) A bond with a low or zero coupon rate may have negative key rate durations for horizons other than the bonds maturity. This is evidenced by some negative key rate durations for 1-2% coupon bonds 4) A callable bond with a low coupon rate is unlikely to be called; hence the bonds maturity matched rate is the most critical rate (i.e the highest key rate duration corresponds to the bonds maturity) 5) All else equal, higher coupon bonds are more likely to be called, and therefore the time to exercise rate will tend to dominate the time to maturity rate 6) Putable bonds with high coupon rates are unlikely to be put, and thus are more sensitive to their maturity matched rates. 7) All else equal, lower coupon bonds are more likely to be put, and therefore the time to exercise rate will tend to dominate the time to maturity rate.

3 Important things to remember about FRAs when pricing and valuing them

1) LIBOR rates in the EuroDollar Market are Add-on rates and are always quoted on a 30/360 day basis in annual terms. For example if the LIBOR quote on 30-day Loan = 6%, the actual unannualized monthly rate is 6% * (30/360) = .5% 2) The Long position in an FRA is, in effect, Long the rate and benefits when the rate increases 3) Although the interest on the underlying loan wont be paid until the end of the loan, the payoff on the FRA occurs at the Expiration of the FRA. Therefore the payoff of the FRA is the Present Value of the interest savings on the loan

VaR has three components

1) Loss Size 2) Probability of a loss that is >= Loss Size 3) Time frame

The In-Kind creation/redemption process for ETFs serves these purposes:

1) Lower cost: The creation/redemption process does not force the ETF manager to sell/purchase portfolio investments; the manager does not incur and resulting transaction costs. The manager usually collects a service charge from the AP to cover any incidentals 2) Tax efficiency: A major benefit of the In-kind creation/ redemption process is that it is not a taxable event. For a mutual fund, liquidity needs for redemption are often met by the fund manager by selling some of the funds holdings, which triggers transaction costs as well as potential cap gains tax. 3) Keeping market prices in line with NAV: APs will engage in arb if the ETF trade at a price significantly different from their NAV. If the ETF trades at a premium, APs can sell the ETF, purchase the creation basket, an recreate those shares....

Due diligence of PE fund investors

1) PE funds have returns that tend to persist. Hence a funds past performance is useful info. 2) Return discrepency between outperformers and underperformers is very large and can be as much as 20% 3) PE investments are usually illiquid, long term investments. The duration of a PE investment, however, is usually shorter than expected

Advantages of reduced form models

1) RF models do not assume that the assets of a company trade 2) Default intensity is allowed to vary as company fundamentals change, as well as when the state of the economy changes

Disadvantages of Reduced Form models

1) RF models do not explain why default occurs 2) Under RF models, default is treated as a random event, but in reality, default is rarely a surprise, and is often predicted by several credit downgrades

Subtypes of Equity REITs

1) Retail or shopping centers: Lease rates and sales per sq foot are important factors to analyze 2) Office reit: analysts must consider property location, convenience, and access to transportation, and the quality of the space including the condition of the building 3) residential REIT; Factors to consider are local demographics, availability of subs, any rent controls imposed by local governments, age of properties, impact of rising costs must be considered 4) health care reits; health care reits are usually unaffected by the economy, however government funding, demographic shifts, new construction v demand, increases in costs of insurance, and potentials for lawsuits persist. 5) Industrial REITs; usually less cyclical; new properties coming onto the market and demand for such space by tenants will affect the value of existing properties 6) Hotel REITs; like healthcare reits, they usually lease properties to management companies, so the reit receives only passive rental income 7) Storage reits; important factors to consider are local factors that drive demand for storage, such as housing sales, new business start ups, demographic trends 8) Diversified reits

Components of return for a private equity investment are

1) Return on the preference shares for PE firm 2) The increased multiple upon exit 3) reduction in the debt claim

Assumptions underlying the Black-Scholes-Merton model

1) The Underlying asset price follows a geometric Brownian motion process. the asset price therefore has a lognormal distribution. In other words, the continuously compounded return is normally distributed. Under this framework change in asset price is continuous 2) The risk free rate is constant and known. Borrowing and lending are both at the risk free rate 3) Volatility of the returns on the underlying asset is constant and known. the price of the underlying asset changes smoothly 4) Markets are 'frictionless' There are no taxes, no transaction costs, and no restrictions on short selling 5) The yield on the underlying asset is constant 6) The options are euro options

The underlying process for calibrating a Binomial Interest Rate tree

1) The interest rate tree should generate arbitrage free values for the benchmark security 2) As stated earlier, adjacent forward rates are two standard deviations apart (e^(2*st.d) 3)The middle forward rate in a period is approx equal to the implied (From the becnhmark spot curve) one period forward rate for that period

3 main inputs for a LBO model

1) The target company's forecasted cash flows 2) The expected returns to the providers of the financing 3) the total amount of financing

Two types of arbitrage Opportunities

1) Value additivity: when the value of whole differs from the sum of the values of parts 2) Dominance: When one asset trades at a lower price than another asset with identical characteristics

Issues in calculating NAV

1) if NAV is only adjusted when there are subsequent rounds of financing, then the NAV will be more stale when financings are infrequent 2) There is no definitive method for calculating NAV for a PE fund because the market value of the portfolio companies is usually not certain until exit 3) Undrawn LP capital commitments are not included in the NAV calc. but are essentially liabilities for the LP. The value of the commitments depends on the cash flows generated from them, but these are quite uncertain. When a GP has trouble raising funds, this implies that the value of these commitments are low 4) The investor should be aware that funds with different strats and maturities may use different valuation methods 5) It is usually the GP who values the fund. LPs are increasingly using 3rd parties to do the valuation

Sources of premiums or discounts for an ETF include

1) timing differences. ETF on foreign securities may experience gaps between the time the ETF is traded and the time when the underlying trades in a foreign market. 2) Stale pricing: Infrequently traded ETFs may reflect noncurrent prices and therefore, their value may differ from the NAV

Embedded Options in a bond allow an issuer to

1)Manage interest rate risk 2) issue bonds with an attractive coupon rate

3 VaR Models:

1)Parametric or variance covariance method -- uses assumption of normality 2) Historical simulation method-- based on actual periodic changes in risk factors 3)Monte Carlo Simulation: based on an assumed probability distribution for each risk factor. Additionally, and assumption must be made about the correlations between risk factors. This procedure is repeated 1000s of times.

Expected Return on a Bond will equal the bonds YTM only when...:

1)The bond is held to maturity 2)All payments are made on time and in full 3)All coupons are reinvested at the YTM

LIBOR day convention

360-day

Loss Given Default (LGD)

= Loss Severity * Exposure

Put payoff for interest rate option

= Notional principal * [MAX(0, Exercise Rate - Reference Rate)] increase in value when rates decrease

Call payoff for interest rate option

= Notional principal * [MAX{0, Reference Rate - Exercise Rate)]

TED Spread =

=3 month Libor Rate - 3 month T-bill Rate

Default Intensity

A key input for Reduced Form models; it is the probability of default over the next (small) time period. Default intensity can be estimated using regression models.

Key rate duration

A more precise method to quantify bond price sensitivity to interest rates is key rate duration. Compared to effective duration, key rate duration is superior for measuring the impact of nonparallel yield curve shifts Key rate duration is the sensitivity of the value of a security (or bond port) to changes in a single par rate, holding all other spot rates constant. In other words, key rate duration isolates price sensitivity to a change in the yield at a particular maturity only Key rate duration is defined as the approximate percentage change in the value of a bond portfolio in response to a 100 basis point change in the corresponding key rate, holding all other rates constant

Fundamental factor model example

A multi factor model to evaluate style and size exposure

Excess return swap

A party may make a single payment at the initiation of the swap and then receive periodic payments of any percentage by which the commodity price exceeds some fixed or benchmark value, times the notional value of the swap. In months in which the commodity price does not exceed fixed value, no payments are made

Equivalencies of a Swaption

A receiver swap can be replicated using a Long receiver swaption and a short payer swaption with the same exercise rates. Conversely a oayer swap can be replicated using a long payer swaption and a short receiver swaption with the same exercise rates. If the exercise rate is set such that the values of the payer and receiver swaption are equal, then the exercise rate must be equal to the market swap fixed rate A long callable bond can be replicated using a Long option free bong plus a short receiver option

Under the Structural Model, Risky Debt can be thought of as equivalent to a portfolio comprising a long position in a Risk free bond and:

A short Put Option on Assets of the company, with a strike price equal to facevalue of debt

Liquidity Preference Theory of term structures

Addresses the short comings of the pure expectations theory by proposing that forward rates reflect investors expectations of future spot rates, plus a liquidity premium to compensate investors for exposure to interest rate risk. Furthermore, the theory suggests that this liquidity premium is positively related to maturity Thus the liquidity preference theory states that forward rates are biased estimates of the markets expectation of future rates because they include a liquidity premium Therefore a Positive sloping yield curve may indicate that either; 1) the market expects future interest rates to rise 2) Rates are expected to remain constant(or even fall) but the addition of the liquidity premium results in a positive slope. A down ward sloping yield curve indicates steeply falling short term interest rates according to the Liquidity Preference Theory Size of liquidity premium do not need to be constant over time

Hazard rate

Affects both the premium leg and protection leg

Extendible Bond

Allows the investor to extend the maturity of the bond, it can be evaluated as a putable bond with a longer maturity

Preferred Habitat Theory

Also proposes that forward rates represent expected future spot rates plus a premium; but it does not support the view that this premium is directly related to maturity Instead it suggests that the existence of an imbalance between the supply and demand for funds in a given maturity range will induce lenders and borrowers to shift from their preferred habitats (Maturity ranges) to one that has the opposite imbalance. However, to entice investors to do so, the investors must be offered an incentive to compensate for the exposure to price and or reinvestment rate risk in the less than preferred habitat. Borrowers require cost savings (i.e ;lower yields) and lenders require a yield premium (i.e higher yields) to move out of their preferred habitats Under this theory, premiums are related to supply and demand for funds at various maturities. Unlike the Liquidity preference theory, under the preferred habitat theory, a 10-year bond might have a higher or lower risk premium than the 25-year bond. It also means that the preferred habitat theory can be used to explain almost any yield curve shape

economic capital

Amount of capital a firm needs to hold for it to survive severe losses due to the risks in its business

Index Credit Default Swap

An Index CDS covers multiple issuers, allowing market participants to take on an exposure to the credit risk of several companies simultaneously in the same way that a stock index allows one to. The protection for each issuer is equal (Equally weighted) and the total notional principal is the sum of the protection on all the issuers

A decrease in interest rate volatility will decrease the value of:

An embedded short call on a bond (But have no effect on the value of the embedded call on the stock) and Increase the Value of the Convertible bond

Riding the Yield Curve

An investor will purchase bonds with maturities longer than investment horizon in hopes that the yield curve wont change, and they can sell the bonds for a capital gain prior to maturity

Investing in a Noncallable, Nonputable Convertible bond is the same as buying:

An option free bond and a call option on an amount of common stock that is equal to the Conversion ratio

Swaptions

An option that gives the holder the right to enter in an Interest Rate Swap Payer Swaption: Is the right to enter into a specific swap at some date in the future at a predetermined rate as the FIXED RATE PAYER Receiver Swaption: is the FLOAT PAYER As interest rates increase; the right to take the Pay-Fixed (A payer swaption) side of a swap becomes more valuable. The holder of a receiver would exercise if the market rates are less than the exercise rate at expiration A swaption is = an option on a series of cash flows (annuity), one for each settlement date of the underlying swap, equal to the difference between the exercise rate on the swap and the market swap fixed rate

Forward Rate

Annualized interest rate om a loan to be initiated at a future period

Hypothetical scenario

Any set of changes in risk factors can be used

Historical scenario

Approach uses a set of changes in risk factors that have actually occurred in the past

Binomial Interest Rate Tree Framework

Assumes interest rates have an equal probability of taking 1 of 2 possible values in the next period

Macroeconomic Factor Model:

Assumes that asset returns are explained by surprises in macro risk factors. Factor surprises are defined as the difference between the realized value of the factor and its consensus predicted value (Macro variables represent the probability of a surprise)

Equilibrium Interest rate term structure models

Attempt to describe changes in term structure through the use of fundamental economic variables that drive interest rates

Modern Term structure Interest Rate Model

Attempts to capture statistical properties of interest rate movements and provides with quantitatively precise descriptions of how interest rates will change

A credit event (i.e default) will occur when

Bankruptcy occurs: A bankruptcy protection filing allows the defaulting party to work with creditors under the supervisions of the court so as to avoid full liquidation Failure to pay: Restructuring

The Cox-Ingersoll-Ross Model

Based on the idea that interest rate movements are driven by individuals choosing between consumption today versus investing and consuming at a time later

Theory of storage for Futures return

Based on the idea that whether a futures market is backwardated or in contango depends on the relationship between the costs of storing the commodity for future use and the benefits of holding the comodity inventory. When the costs of storage outweigh the benefits for holding inventory, futures are more attractive than current inventory, futures will trade at a higher price than spot, and market is in contango When the benefits of holding inventory > costs of storage, market is backwardated and spot prices are greater than futures

If default probabilities are expected to be higher (Or recovery rates Lower) in the future the credit curve would be expected to

Be positively sloped Flat credit curves indicate stable expectations over time

Arbitrage free models

Begin with the assumption that bonds trading in the market are correctly priced. These models do not try to justify the current yield curve; rather they take the curve as given The ability to calibrate arb free models to match current market prices is one advantage over equilibrium models

Commerical real estate investments have:

Bond like charactoristics: The steady rental income stream is similar to cash flows from a portfolio of obnds. Furthermore, just as the credit quality of issuers affect the value of a bond portfolio, the credit quality of tenants also affects the value of commercial real estate Equity like characteristics: The value of commercial real estate is influenced by many factors, including the state of the economy, the demand for rental properties, and property location. Uncertainty about the value of the property at the end of the lease term gives it this characteristic Illiquidity

Option Adjusted Spread rules (OAS)

Bonds with similar credit risks should have identical OAS If the OAS for a bond is higher than the OAS of its peers, bond is undervalued If the OAS for a bond is lower than the OAS of its peers, the bond is Overvalued

A synthetic Euro put option is created by:

Buying the discount bond, buying the call option, and short selling the stock

Steps for valuing an option with a Two-Period Binomial Model

Calculate the stocks value at the end of the two periods (There are three possible outcomes, because an up the down move gets the same place as a down then up move) Calculate the three possible option payoffs at the end of two periods Calculate the expected option payoff at the end of two periods using the up and down move probabilities Discount the expected option payoff (t=2) back one period at the risk free rate to find the option values at the end of the first period (t=1) Calculate the expected option value at the end of period 1 using the up and down move probabilities Discount the expected option value at the end of one period back one period at the rf rate to find the option value today (T=0)

We can calculate the value of an option on a stock by:

Calculating the payoff of the option at maturity in both the up move and down move states Calculating the expected value of the option in one year as the probability weighted average of the payoffs in each state Discounting the expected value back to today at the risk free rate

Option Value related to interest rates:

Call option value is Inversely related to the level of Interest Rates Put option value varies directly with the level of interest rates

Negative convexity occurs in

Callable bonds, due to a decline in interest rates when rates are already low, therefore a decline in rates is not likely to result in best price performance for a callable bond

When an Upward Sloping yield curve (normal) flattens, Options do what on Bonds

Calls increase in value while put options decrease in value

Transaction based indicies

Can be constructed using a repeat sales index and a hedonic index Repeat-Sales Index: relies on repeat sales of the same property Hedonic Index: requires only one sale, a regression is developed to control for differences in property characteristics such as size age location and so forth

Implementation shortfall

Captures the Price impact, Delay (slippage) and opportunity cost of a trade

Waterfall Methods for distribution: Deal by Deal

Carried interest can be distributed after each individual deal, therefore, carried interest payout = Carried interest % * profit

Water fall methods for distribution: Total Return method #1

Carried interest can only be paid after the Portfolio value exceeds Committed Capital.

Water fall methods for Distribution: Total Return method #2

Carriedi nterest can be paid when the value of the portfolio exceeds Invested Capital by some minimum amount To find that amount take Invested capital * 1+ threshold

Appraisal based Indicies

Combine valuations of individual properties that can be used to measure market movement

Other considerations for Valuing Private Equity Portfolio Companies

Control premiums countries risk marketability illiquidity

Types of ETF risk:

Counterparty risk Settlement risk Security lending Fund closures Expectation-related risk

Valuation of an option free bond using Pathwise Valuation

Create paths for the maturity of the bond, ex: 3 years, for each year you will trace out what interest rates will be used, and then to get the value for the year, you will sum up the (coupon / 1+r) Ex: for a 3 year 3% coup on $100 par V1 = 3/1.03+3/1.03*1.05783 + 103 / 1.03* 1.057883 * 1.107383

Credit ratings incorporate both

Default probability and loss given default

Delta

Describes the relationship between changes in asset prices and changes in option prices. Delta is also the Hedge Ratio Call option deltas are Positive because as the underlying asset price increases, call options value increase. The delta of a Put option is Negative because as put value falls, asset prices increase Delta is the slope of the Prior to expiration curve

In credit rating, the practice of notching accounts for:

Differences in Loss Given Default

Common errors made using the DCF method

Discount rate does not adequately capture risk. Income growth exceeds expense growth The terminal Cap rate and the going-in cap rate are not consistent The terminal cap rate is applied to NOI that is atypical The cyclicality of real estate markets is ignored

Reduced form models of corporate credit risk

Do not rely on the structure of a company's balance sheet, and therefore, do not assume that the assets of the company trade. Unlike structural models, reduced form models do NOT explain why default occurs They explain WHEN default occurs

One-Sided Duration

Durations that apply only when interest rates rise (or only when rates fall) -- are better are capturing interest rate sensitivity than simple effective duration

Compare Effective Duration callable, putable, and straight bonds

Effective duration (Callable) <= Effective Duration (straight) Effective Duration (Putable) <= EffDur (straight) EffDur(Zero coup) = Maturity of bond (approx) EffDur of Fixed rate coup bond < Maturity of bond Effdur of Floater (approx) = Time (in years) to next reset

Securitized Debt

Entails financing of specific assets (e.g auto loans, credit card receivables, and mortgages). Secured debt is usually financed via bankruptcy remote entities SPE's

Stress Test

Exaimine the effect on value (or solvency) of a scenario of extreme risk factor changes

investment Characteristic's of REITS

Exemption from corporate level income tax High dividend yield Low income volatility Secondary equity offerings

Exit value for buyouts in private equity port company's

Exit Value = Investment cost + earnings growth + increase in price multiple + reduction in debt

Conditional VaR; CVaR

Expected loss given that the loss is equal to or greater than VaR

Value of bond using Z-Spread example

First Step 1) Derive Spot Rates; - (1+S2)^2= (1+s1)*[1+f(1,1)] - (1+S3)^3 = (1+s2)*[1+f(1,1)]*[1+f(2,1)] Next Step 2) Compute bonds price using PV (DDM) HOWEVER, the formula using Z spread = PV = SUM(Coupon / (1+r+Z-spread)^t) + ((Coupon + Face Value) / (1+r+z)^T

Active ETF strategies are most likely to be used for

Fixed income rather than for equity investments due to the low liquidity of most fixed income securities

Sensitivity analysis

Focuses on the effect on portfolio value given a small change in One risk factor

Covered Bonds are most likely issued by a financial institution and?

Have recourse rights as well as backing of the collateral pool Covered bonds are senior, secured bonds issued by a financial institution. Covered bonds are backed by a collateral pool as well as by the issuer

Implications for the Shape of the Yield Curve under the Pure Expectations Theory are:

If the Yield Curve is upward Sloping, Short Term rates are expected to rise If the curve is downward sloping, short term rates are expected to fall A flat yield curve implies that the market expects short term rates to remain constant

How options on Interest Rates work

Interest rate options are options on Forward Rate agreements (FRA's). A call on an FRA Gains when Rates Rise A put on an FRA Gains when Rates Lower Interest rates are fixed in advanced and settles in arrears (i.e paid at maturity of the loan) While usually FRA use a 30/360 convention Options on an FRA use the 30/365 convention

Examples of Credit Enhancements:

Internal Include trenching of credit risk among classes with differing seniority (i.e distribution waterfall), Overcollateralization, and excess servicing spread (whereby such excess collateral or spread becomes the first line of defense against credit losses). External Third party guarantees (e.g bank, insurance comps, loan originators) are exampled of external credit enhancements

Unbiased Expectations Theory (Pure expectations)

Investors expectations that determine the shape of the Interest Rate Term Structure; Specifically, this theory suggests that forward rates are solely a function of expected future spot rates and that every maturity strategy has the same expected return over the given investment horizon In other words, long term interest rates equal the mean of future expected short term rates This implies that an investor should earn the same return by investing in a five year bond that will be sold two years prior to maturity Investors demand a risk premium for maturity strategies that differ from their investment horizon

Implementation shortfal

Is a conceptual approach that measures transaction costs as the difference between the value of the actual portfolio and the value of a hypothetical paper portfolio. In a paper portfolio, the trade was executed at no cost and at the prevailing price.

Information Coefficient (IC)

Is a measure of a managers skill. IC is the Ex-Ante (i.e expected) risk weighted correlation between active returns and forecasted active returns. The ex post info coefficient, ICr, measures actual correlation between active returns and expected active returns

Marginal VaR MVaR

Is estimated as the slope of a curve that plots VaR as a function of a security's weight in the portfolio. The MVaR is calced at the point on the curve corresponding to the security's current weight, so we can interpret it as the change in VaR for as 1% increase in the security's weight.

Incremental VaR IVaR

Is the change in VaR from a change in the portfolio allocation to a security. If a 2% increase in the weight of a security in the portfolio increases the portfolios VaR from $1,345,600 to $1,562,400 the IVaR for the 2% increase in the portfolio weight is the difference = $216,800

Functional Obsolescence

Is the loss in value resulting from defects in design that impairs a buildings utility. For example, a building might have a bad floor plan, as a result, NOI is usually lower than otherwise would be because of the lower rent or higher operating costs. Functional obsolescence can be estimated by capitalizing the decline in NOI

If an ETF is trading at a price about its iNAV;

It is most likely trading at a Premium

Fundamental Law of Active Management

Its usefulness stems from its ability to separate the expected value added of a portfolio into the contributions of the few basic elements of the strategy

Due diligence for Real estate investors

Lease review and rental history Confirm the operating expenses by examining bills Review cash flow statements Obtain an environmental report to identify the possibility of contamination Perform a physical/engineering inspection to ID structural issues and check conditions of building systems Inspect the title and other legal documents for deficiencies Have the property surveyed to confirm the boundaries and identify easements Verify compliance with zoning laws, building codes, and environmental regulations

Disadvantages that apply only to REITS, but not REOCS

Limited potential for Income growth Forced Equity issuance Lack of flexibility

General risk factors of investing in PE

Liquidity risk Unquoted investment risk Competitive environment risk Agency risk Capital risk Regulatory risk tax risk valuation risk Diversification risk Market risk

Protective put =

Long Stock and Long Put

Fiduciary call =

Long call plus an investment in a zero coupon bond with F.V = Stike price

Effective Duration

Measures price sensitivity to small PARALLEL shifts in the yield curve. It is important to note that effective duration is not an accurate measure of interest rate sensitivity to Non-Parallel shifts in the yield curve, Shaping risk refers to changes in portfolio value due to changes in the shape of the benchmark yield curve

Ex Ante Tracking error, or Relative VaR

Measures the VaR of the difference between the return on a portfolio and the return on its managers benchmark portfolio. A 5% monthly relative VaR of 2.5% implies that 5% of the time, the portfolios relative underperformance will be at least 2.5%. The relative VaR can be calculated as the VaR of a combination of long positions in hte subject portfolio and a short position in the benchmark portfolio.

Modified Duration

Measures the bonds price sensitivity to changes in interest rates, assuming that the bonds cashflows do not change as interest rates change

Gama

Measures the rate of change in Delta Gamma captures the curvature of the option value versus stock price relationship Long positions in calls and puts have Positive Gama. For example, a gamma of .04 implies that a $1.00 increase in the price of the underlying stock will cause a call options delta to increase by .04, making the call option more sensitive to changes in stock price Gamma is highest for At-The-Money Options. Deep in the money or Deep out of the money options have Low Gamma. Gamma changes with stock prices and with time to expiration. To lower (inc) the overall Gamma in a portfolio, one should short (go long) Options

Theta

Measures the sensitivity of option prices to passage of time. As time passes, and a call option approaches maturity its speculative value declines; called Time Decay This is similar to puts, however deep in the money puts near maturity can increase in value Because theta is a measure of Time decay, it is less than zero as time passes and an option approaches maturity

Rho

Measures the sensitivity of the option price to changes in the risk free rate. Call option value increases aa the RF rate increases Put option value decreases as the RF rate increase

The Ho-Lee Model

Model assumes that changes in the yield curve are consistent with a no arbitrage condition This model is calibrated by using market prices to find the time dependent drift term 0t, that generates the current term structure. The Ho-Lee model can be used to price zero coupon bonds and to determine spot curve. The model produces a symmetrical distribution of future rates

Regarding volatility of term structure, research indicates that volatility in short term rates is most strongly linked to uncertainty regarding:

Monetary policy

When measuring Value Added by active management, it is most accurate to state that the active weights in an actively managed portfolio :

Must be positively correlated with realized asset returns for value added to be positive

Economic Value Determinants of REITs

National GDP growth is the largest driver of economic value for all REIT types. Overall growth in the economy means more jobs, more need for office space, more disposable income, more growth in shopping centers, more demand for hotel rooms from business and leisure travelers and so on

Market Fragmentation

Occurs when a security trades in multiple markets. There may be significant liquidity differences between these markets.

Economic Obsolescence

Occurs when new construction is not feasible under current economic conditions

Locational Obsolescence

Occurs when the location is no longer optimal.

Total value of a building =

P.V of term rent + PV of Incremental rent

Upfront payment (By protection buyer) =

P.V(Protection Leg) - P.V(Premium leg)

Quantitative Measures of a PE firm

Paid In Capital (PIC): Capital utilized by GP Distributed to paid in capital (DPI): This measures the LPs realized returns, and is cumulative distributions paid to the LPs dividend by the Cumulative invested capital. It is net of fees and carried interest, also called Cash on cash return Residual Value to paid in capital (RVPI): This measures the LP's unrealized return and is the value of the LPs holdings in the fund / cumulative invested capital. Net of fees and carried interest Total value to paid in capital (TVPI): This measures the LP's realized and unrealized return and is the sum of DPI and RVPI. It is net of fees and carried interest

Four major economic factors that impact REITS

Population growth, Job creation, new space supply Vs. Demand, Retail sales growth

Arbitrage gap

Price band of the NAV of an ETF Arb gap is negatively correlated with: The liquidity of the securities underlying the index that the etf is trading

The credit spread is positively related to

Probability of default

Factors that influence the pricing of a CDS (I.E the spread on a cds)

Probability of default Loss given default Coupon rate on the swap The CDS spread is higher for Higher Probabilities of default and for higher loss given default

Using the DCF method for Real Estate uses the following estimates and assumptions

Project income from existing leases: It is necessary to track the start and end dates and the various components of each lease. Such as base rent, Index Adjustments, and expense reimbursements from tenants Lease renewal assumptions: may require estimating the probability of renewal Operating expense assumptions: Operating expenses can be classified as fixed, variable, or hybrid of the two. Variable expenses vary with occupancy, while fixed expenses do not. Fixed Expenses can change because of inflation Capital Expenditures and assumptions: Expenditures for CAPEX improvements, such as roof replacement, are lumpy. Consequently some appraisers average the CPAEX and deduct a portion each year instead of actual amount when paid. Vacancy assumptions: It is necessary to estimate how long before currently vacant space is leased Estimated resale price: A holding period that extends beyond the existing leases should be chosen. This will make it easier to estimate the resale price because all leases will reflect current market rents Appropriate discount rates: The discount rate is not directly observable, but some analysts use buyer surveys are guides. the discount rate should be higher than the mortgage rate because there is more risk and should reflect the riskiness of the investment relative to alternatives

Scenario analysis

Provides an estimate of the effect on portfolio value of a set of changes of significant magnitude in multiple risk factors

UPREIT

REIT structure where the reit is the general partner and holds a controlling interest in a partnership that owns and operates a property

Interpolated Rate =

Rate for Lower Bound + [(# of years for interpolated rate - # years for Lower Bound)*(Higher bound rate - Lower Bound Rate)] / (# years for upper bound - # of years for Lower bound)

Yield Curve Risk

Refers to risk to the value of a bond portfolio due to unexpected changes in the yield curve

Replacement cost

Refers to the cost of a building having the same utility constructed with modern building materials. Reproduction costs refers to the cost of reproducing an extra replica of the building using the same materials, design, and quality of construction

Backward Induction

Refers to the process of valuing a bond using a Binomial Interest Rate Tree

Swap Rate Curve

Reflects the credit risk of commercial banks Swap market is not regulated by any government which makes swap rates in different countries comparable Swap curve typically has yield quotes at many maturities

OAS Undervalued over valued rules

Relative to bond A, bond B has a lower OAS. Given that the two bonds have ismilar credit risk, bond B offers a Lower OAS for the same level of risk. Therefore, bond A is more attractive (underpriced) relative to bond B

Due diligence considerations of REITs

Remaining lease terms Inflation protection In-place rents versus market rents Costs to Re lease space tenant concentration in the portfolio Tenants financial health New competition Balance sheet analysis Quality of management

High Coupon Puttable bonds are Unlikely to be put, therefore their Key rate duration would

Respond to their time to maturity

Highest and best use

Revolves around what potential property has the highest implied Land Value

Roll yield or Roll return is positive and negative when

Roll yield is positive if the futures price curve is backwardated Roll yield is Negative when the futures Price Curve is in Contango

Key differences between Macroeconomic Factor model and the Fundamental Factor Model:

Sensitivities: The standardized sensitivities in the Fundamental Factor Model (bi1, bi2) are calculated directly from the attribute (e.g P/E) Data-- they are not estimates. This contrasts with the Macroeconomic model in which the sensitivities are regression slope estimates Interpretation of Factors: The macroeconomic factors (Fgdp and Fqs) are surprises in the macro variables (e.g inflation or stock shock) In contrast the fundamental model factors (Fp/e and Fsize) are rates of return associated with each factor and are estimated using a multiple regression Intercept Term: The intercept in the macroeconomic model equates the stocks expected return (based on market consensus of the expectations of the macro factors) from an equilibrium pricing model like the APT. In contrast the Intercept of the Fundamental value model with standardized sensitivities has no economic interpretation; it is simply the regression intercept necessary to make unsystematic risk of asset = 0

The protection buyers of a CDS is:

Short Credit risk and hence benefits when the credit spread widens

Local Expectations Theory (Does not hold)

Similar to unbiased theory, but this theory preserves the risk neutrality assumption; ONLY for short holding periods. In other words, over longer periods, risk premiums exists. This implies that over the short term (even risky long maturity bonds) will earn the Risk free Rate

Busted Convertible

Sometimes the price of the common stock associated with a convertible issue is so low that it has little or no effect on the convertibles market price, the bond trades as though it is a straight bond

Insurance theory for Futures return

States that the desire of commodity producers to reduce their price risk drives commodity futures return. producers face uncertainty about the price they will receive for their output and reduce this uncertainty by selling futures contracts. The selling drives down the price. The insurance theory states that the futures prices will be less than current spot prices to provide a return to those buying futures from producers

Forward Pricing Model Steps

Step 1) Calculate the Discount Factors; discount factor = pt= 1/(1+Spot)^T Step 2) Calculate the Forward Price as of Today Forward Price = F(j,k) = P(j+k)/Pj

Steps for Calculating an FRA before Settlement date

Step 1) Find the "New" FRA price on the X-day Loan, T- X days from now, at the current x-day rate Step 2) Calculate the Interest Difference on the principal amount for the new loan compared to the old loan then multiply it by notional Step 3) Discount the amount of interest difference at the rate that makes the difference between new and old FRA ,maturity wise, equate

Steps to value a Currency swap AFTER initiation

Step 1) First calculate the discount factors for the period that changed for both currencies; in this example it a 5m swap, you want to take the equivalent of a bond, that makes a coupon payment in X days of (Principal of bond * quarterly rate). This amount of the bond + coupon is then discounted to the present using the correct discount factor for the currency Step 2) Next calculate the value after X days on the opposite currency side doing the same as above. 3)Then convert the bond + coupon discounted to the correct currency, and to get the value of the received currency, subtract the two in the same currency to get the difference

Steps for Calculating Effective Duration and effective convexity

Step 1) Given assumptions about benchmark rates, interest rate vol, and any call/puts, calculate the OAS for the issue using the current market price and the binomial model Step 2) Impose a small parallel shift in the benchmark yield curve by an amount equal to +Change Y Step 3) Build a new binomial interest rate tree using the new yield curve Step 4) Add the OAS from step 1 to each of the 1 year rates in the IRT to get a Modified tree Step 5) Compute the BV+ChangeY using modified tree Step 6) Repeat steps 2-5 using a parallel shift of - change Y to obtain the value of BV-ChangeY

Calculations using the NPV Venture Capital Method and a Single Financing round

Step 1) The Post- Money (POST) Valuation is the Present value of expected exit value. Step 2) Calculate PRE; PRE is what the company would hypothetically be worth without investment = POST - Capital investment Step 3) Calc f; f = F.V(INV) / POST f represents the % of the firm the VC must own Step 4) Calc SharesVC = Shares (founder) * (f/1-f) Step 5) Calc P; P = INV / Shares (vc)

Compare effective convexity of callable, putable, and straight bonds

Straight Bonds have positive effective Convexity: The increase in the value of an option free bond is higher when rates fall than the decrease in the value when rates increase by an equal amount. When rates are high, callable bonds are unlikely to be called and will exhibit positive convexity. When the underlying call option is near the money, its effective convexity turns negative; the upside potential of the bonds price is limited due to the call (While downside is not protected). Putable bonds exhibit convexity throughout

What has positive convexity at all interest rate levels?

Straight and Putable Bonds

Which bond tends to have highest effective duration?

Straight bonds, tend to have higher EffDurs than bonds with embedded options

Vasicek Model (interest Rates)

Suggests that interest rates are mean reverting to some long run value Main disadvantage is that this model does not force interest rates to be non-negative

Swap Spread =

Swap Spreadt= Swap Rate t - Treasury Yield t

Transfer coefficient

TC; can be though of as the correlation between actual active weights and optimal active weights. The optimal active weight for a security is positively related to its expected active return and negatively related to its expected active risk

A highly risk averse trader seeking to profit from mispricing across markets would most likely:

Take liquidity on both markets

Following Advantages of REITS, not REOCS

Tax exempt, predictable earnings, high yield

Forward Curve

Term structure of Forward Rates

I - Spread

The I spread for a credit risky bond is the amount by which the Yield on the Risky Bond exceeds the Swap Rate for the Same Maturity

Protection Leg

The Premium Leg + the protection seller's payments to the protection buyer in case of default

An interest rate call option has a positive payoff when:

The Reference Rate > Exercise Rate Interest rate calls increase in value when rates increase

If the CDS coupon Rate is higher than the credit spread

The Seller of the CDS will be paying an upfront premium

Par Rate

The YTM of a bond trading at par

Spot Rate T

The YTM of a zero coupon bond with a maturity, T

TED Spread

The amount by which the Interest Rates on Loans between banks (3 month LIBOR), Exceeds the interest rate on Short term U.S government Debt (3 months) T stands for T-bill ED stands for the ticker symbol for the Eurodollar futures Seen as the risk between interbank Loans

Expected Exposure is

The amount of money a bond investor in a credit risky bond stands to lose at a point in time before any recovers is factored in

Expected Exposure

The amount of money a bond investor in a credit risky bond stands to lose at a point in time before any recovery is factored in

Convenience Yield

The benefits of having physical inventory available When physical stocks are low there is a high probability that the commodity will be in short supply. The benefits of holding physical stock are higher

When assumed volatility in a binomial tree increases:

The computed value of OAS will decrease. When an analyst uses a lower than actual level of volatility, the computed OAS for a Callable Bond will be too High. OAS spread decrease as implied volatility increases

Advantages of VaR

The concept of VaR is simple and easy to explain VaR allows the risk of different portfolios, asset classes, or trading operations to be compared to gain a sense of relative risk VaR can be used for performance evaluations When allocating capital to various trading units, a firms risk managers can also look at the allocation of VaR and optimize the allocation of capital given the firms determination of the maximum VaR that the organization should be exposed to Global banking regulators accept VaR as a measure of financial risk Reliability of VaR can be verified Via back testing

Break even inflation rate

The difference between the yield on a Non inflation indexed risk free bond and the yield on an inflation indexed risk free bond of the same maturity

When the Yield Curve is Downward Sloping, the Forward Curve is most likely to be:

The forward curve is most likely to be below the spot (yield) curve

When the Yield (spot) curve is Upward Sloping, the Forward Curve will most likely be

The forward curve will most likely lie above the spot (yield) curve

When Spot Rates turn out to be Lower (higher) than the Forward Rate curve implied #'s,

The forward price Increases (Decreases)

Discounted Cash Flow Method for real estate

The future cash flows including the CAPEX and Terminal Value are projected over the holding period and discounted to the present at a discount rate. Future growth of NOI is explicit in the DCF method

The minimum Value of a Convertible Bond is

The greater of its conversion value or its straight value

Key points about Real Risk Free Rate and the Inter-Temporal Rate of substitution

The higher the utility investors attach for current consumption relative to future consumption, the higher the real risk free rate will be Diminishing marginal utility of wealth means that an investors marginal utility of consumption declines as wealth increases. This suggests that marginal utility of consumption is higher during periods of scarcity If investors expect higher incomes in the future, their expected marginal utility of future consumption is decreased relative to current consumption. When investors expectations about the economy change to better economic times ahead, the expectation of higher incomes in the future will lead to an increase in current consumption relative to future consumption and would therefore save less. conversely investors expecting worse time ahead would prefer to increase future consumption by reducing current consumption and saving more Investors increase their savings rate when expected returns are higher or when uncertainty about their future income increases

The portfolio with the highest information ratio will also be the portfolio with

The highest sharpe ratio

Principal risks of REITs

The most risky REITs are those that invest in property sectors where significant mismatch between supply and demance are likely (particularly healthcare, hotels, and office reits), as well as those sectors where the occupancy rates are most likely to fluctuate within a short period of time. Also risks appear from riskiness of the properties in place

The Long Position in an FRA is:

The party that is effectively borrowing money (Long the loan, with the contract price being the interest rate on the loan) If the floating rate at contract expiration is above the specified rate in the FRA, the long position in the contract can be viewed as the right to borrow at below market rates, and the long will receive a payment. If the floating rate at expiration date is below the rate specified in the contract, the short will receive a cash payment from the long

Premium Leg

The payments made by the protection buyer to the seller of a CDS

Recovery rate

The percentage recovered in the event of default (Opposite of loss severity)

maximum quoted spread on an ETF is most likely to be Negative when

The probability of completing an offsetting trade in the secondary market

Hazard Rate

The probability of default given that default has not already occurred The credit risk of a reference obligation and hence the cost of protection is proportional to the hazard rate

The Hazard Rate is

The probability of default in year 1, the probability of default will be less than the hazard rate in all years after year 1

Qualitative aspects of fund to analyze for a PE investment

The realized investments, with and evaluation of success and failures The unrealized investments with an evaluation of exit horizons and potential problems cash flow projections at the fund and portfolio company level fund valuation, NAV and fin statements

The credit spread is Inversely related to

The recovery rate

DOWNREIT

The reit has an ownership interest in more than one partnership and can own properties both at the partnership level and at the reit level

Node Relationship for Binomial Trees

The relationship among the set of rates associated with each individual nodal period is a function of the interest rate volatility assumed to generate the tree. Volatility estimates can be based on historical data or can be implied Volatility derived from interest rate derivatives The Binomial Interest Rate tree Framework is a Lognormal Random Walk Model with Two desirable properties 1) Higher Volatility at higher rates 2) Non Negative interest rates

The term structure of credit spreads shows:

The relationship between credit spreads and maturity

Spot Yield Curve

The term structure of Spot Rates versus T, Maturity

Commodity Volatility Swap

The underlying factor is the volatility of the commodity price. If the volatility of the price is higher than the expected level of volatility specified in the swap, the volatility buyer receives a payment. When actual Vol. is Lower, than specified level, the Vol seller receives payment

An option on a Futures contract can be thought as the following:

The value of a call option on futures is equal to the value of a portfolio with a long futures position (the PV of the futures price multiples by N(d1)) and a short bond position (The pv of the exercise price multiplied by N(d2)) The value of a put option is equal to the value of a portfolioo with a long bond and a short futures position The value of a Call can also be thought as of the present value of the difference between the futures price (ADJUSTED BY n(D1)) and the exercise price (adjusted by N(d2))

Basis Swap

The variable payments are based on the difference between the prices of two commodities. often the two commodities are one that has liquid traded futures available for hedging and the other with no liquid futures contracts available. because the price changes of the two commodities are less than perfectly correlated, the difference between them (the basis) changes over time. By combining a hedge using the liquid futures with a basis swap, the swap buyer can hedge the price risk he faces from the input that does not have a liquid futures market

Option values on bonds are positively related to:

The volatility of their underlying. When interest rate volatility increases, the value of both call and put options increase

Hedging Pressure Hypothesis for Futures return

This theory expands on the Insurance theory. It adds hedging behavior of commodity consumers to the insurance theory.

Market Fragmentation

Trading algo such as smart order routing and liquidity aggregation seek to overcome the challenges posed by market fragmentation. These automated strategies are seeking out liquidity across markets

Costs of a P.E investment

Transaction costs Investment vehicle fund setup cost admin cost audit cost Management and performance costs Dilution costs Placement fees

Traditional (long only ) asset managers

Typically focus on relative risk measures unless their goal is an absolute return target. Typical risk measures used include: The size of a position Sensitivity measures of interest rate and market risk Historical and hypothetical scenario analysis and option risk Active Share: The difference between the weight of a security in the portfolio and its weight in the benchmark

Direct Capitalization Method for real estate

Under this method, a cap rate or income multiplier is applied to first year NOI. Implicit in the cap rate or multiplier is the expected increases in growth

Limitations of VWAP Transaction Costs

VWAP is not useful if the trade being evaluated is a significant part of the trading volume. In such cases, the benchmark VWAP and the trade VWAP will be close to each other VWAP does not capture the price impact cost. For example, if a large buy order was the only trade that was executed during a time interval at a price above the normal trading price, the benchmark VWAP will then be identical to the trade VWAP and the calculated transaction cost will be zero, however, trade was not executed at a good price

Limitation of VaR

VaR estimations require many chjoices and can be very significantly affected by those choices The assumption of normality leads to underestimates of downside risk becuase actual returns distributions frequently have 'fatter tails' than a normal dist. Liquidity often falls significantly when asset prices fall. VaR does not account for this It is well known that correlations increased, or spike during periods of financial stress. Increasing Correlations mean that VaR measures based on normal level of correlation will overestimate diversification benefits While VaR is a single number that can be used to quantify risk, as with any summary measure, many aspects of risk are not quantified or included VaR focuses only on downside risk and extreme negative outcomes

Limitations of Effective Spread

When a large order is split into smaller orders, the effective spread is a poor indicator of trade performance because it does not take into account the price impact of costs Effective spread also does not account for slippage or delay costs when part of the order does not get filled at desired prices Sometimes the market price will move unfavorably, voiding a trading opportunity

Most likely to experience an Increase in EffDur due to an Increase in Interest Rates

When interest rates increase, a callable bond becomes Less Likely to be called (Therefore duration increases). The put option in a putable bond would be more likely to be exercised in a rising interest rate environment, hence the duration of a putable bond would decrease. Duration of an option free bond would also decrease as interest rates increase

The following comparisons can be made between ownership of the underlying stock and the risk return characterisitics of a convertible bond

When the stocks price falls, the returns on convertible bonds exceeds those of the stock, because the convertible bonds price has a floor equal to its straight bond value When the stock price rises, the bond will underperform because of the conversion premium. This is the main drawback of investing in convertible bonds versus investing directly in stocks If the stocks price remains stable, the return on a convertible bond may exceed the stocks return due to the coupon payments received from the bond, assuming no change in interest rates or credit risk affect the issues

Term and reversion approach

Whereby the contract (term) rent and the reversion are appraised separately using different cap rates

Available Commodity Indexes differ in the following dimensions:

Which commodities are included The weighting of the Commodities in the index The method of rolling contracts over as they near expiration The method of rebalancing portfolio weights

Interest rate changes on Effective Duration

While effDur of straight bonds is relatively indifferent by changes in interest rates; an Increase (DEC) in rates would Decrease Effective Duration on a Putable (Callable) bond

Breadth is most likely to be equal to the number of securities multiplied by the number of decision periods per year if active returns are correlated:

With active weights BR is intended to measure the number of independent decisions that an investor makes each years

I Spread =

Yield on bond - Swap Rate

Segmented Markets Theory

Yields are Not Determined by Liquidity premiums and expected spot rates. Rather, the shape of the yield curve is determined by the preferences of borrowers and lenders, which drives the balance between supply of and demand for loans of different maturities. The theory suggests that the yield at each maturity is determined independently of the yields at other maturities; we can think of each maturity to be essentially unrelated to other maturities This theory suggests that various market participants deal in securities of a particular maturity because they are prevented from operating at different maturities

Z-Spread

Zero Volatility Spread, is the spread that when ADDED to each spot rate on the default free spot curve, makes the PV of a Bonds Cash Flows Equal To Bonds Market Price therefore, Z-Spread is the spread over the entire spot rate curve

Structural models of Corporate credit risk

are based on the structure of a company's balance sheet and rely on insight provided by the option pricing theory They explain why default occurs

Fundamental factor models

assume asset returns are explained by multiple firm specific factors (eg. p/e., market cap)

Reconciliation of Value

because of different assumptions and availability of data, the three valuation approaches are likely to yield different value estimates. An important part of the appraisal process involves determining the final estimate of value by reconciling the differences in the three approaches

Prepayment risk differs from call risk by

being affected not only by the level of interest rate at a particular point in time, but also, by the path the rates took to get there

A swap of returns on two different stocks cant be viewed as

buying one stock (receiving returns) and shorting an equal value of another stock (Paying the returns). There is no "Pricing" at swap initiation, and we can value the swap at any point by taking the difference in returns * notional principal

A decrease in stock price volatility will decrease the value of the

embedded call on the stock (But have no effect on the embedded call on the bond) and decrease the value of the convertible bond

The owner of a convertible bond:

has the right to convert the bond into a fixed number of common shares of the issuer during a specified time frame (Conversion period) and at a fixed amount of money (Conversion Price). Convertibles allow inventors to enjoy the upside on the issuers stock, although this comes at a cost of lower yield The issuer of a convertible bond benefits from a lower borrowing cost, but existing shareholders may face dilution if the conversion option is exercised

Estate Put

includes a provision that allows the heirs of an investor to put the bond back to the issuer upon the death of the investor. The value of this contingent put option is inversely related to the investors life expectancy; the shorter the life expectancy the higher the value

Vega

measures the sensitivity of the option price to changes in the volatility of returns on the underlying asset Vega gets larger as the option gets closure to being At the Money

Bermudan-style option

option can be exercised at any time AFTER a lockout period

The modern term structure model that is most likely to precisely generate the current term structure is

the Ho-Lee Model

Statistical factor model

uses statistical methods to explain asset returns. Two primary types of stat models are used: Factor analysis; portfolios that explain covariance in asset returns Principal component models: factors are portfolios that explain the variance in asset returns: Major weakness is that stat factors do not lend themselves well to economic interpretation

Forward Pricing Model

values forward contracts by using an arbitrage argument that equates buying a zero-coupon bond to entering into a forward contract to buy a zero-coupon bond that matures at the same time: P(j+k) = PjF(j,k)