Financial Markets Test 1
Private equity
Collectively, these investments in firms that do not trade on public stock exchanges are known as blank investments.
market value-weighted index
Computed by calculating a weighted average of the returns of each security in the index, with weights proportional to outstanding market value.
Securitization
These pools, which were essentially claims on the underlying mortgages, were soon dubbed mortgage-backed securities, and the process was called
Spot rate
They call the yield to maturity on zero-coupon bonds the spot rate, meaning the rate that prevails today for a time period corresponding to the zero's maturity
investment-grade bond
Those rated BBB or above (S&P, Fitch) or Baa and above (Moody's) are considered investment-grade bonds, whereas lower-rated bonds are classified as speculative-grade or junk bonds. Defaults on low-grade issues are not uncommon.
speculative-grade bond
Those rated BBB or above (S&P, Fitch) or Baa and above (Moody's) are considered investment-grade bonds, whereas lower-rated bonds are classified as speculative-grade or junk bonds. Defaults on low-grade issues are not uncommon.
default premium
To compensate for the possibility of default, corporate bonds must offer a default premium. The default premium is the difference between the promised yield on a corporate bond and the yield of an otherwise-identical government bond that is riskless in terms of default
equivalent taxable yield
To derive this value, we set after-tax yields equal and solve for the equivalent taxable yield of the tax-exempt bond. This is the rate a taxable bond must offer to match the after-tax yield on the tax-free municipal. rtaxable(1− t) = rmuni or rtaxable = rmuni/(1− t) Cutoff tax bracket = 1 − rmuni /rtaxable
sinking fund
To help ensure the commitment does not create a cash flow crisis, the firm agrees to establish a sinking fund to spread the payment burden over several years.
subordination clauses
To prevent firms from harming bondholders in this manner, subordination clauses restrict the amount of additional borrowing. Additional debt might be required to be subordinated in priority to existing debt; that is, in the event of bankruptcy, subordinated or junior debtholders will not be paid unless and until the prior senior debt is fully paid off.
Expected Return
To start, we will characterize probability distributions of rates of return by their expected or mean return, E(r), and standard deviation, σ. The expected rate of return is a probability-weighted average of the rates of return in each scenario. Calling p(s) the probability of each scenario and r(s) the HPR in each scenario, where scenarios are labeled or "indexed" by s, we write the expected return as E(r) = ∑ p(s)r(s)
eurodollars
Dollar-denominated deposits at foreign banks or foreign branches of American banks
Arithmetic average of historic rates of return
E(r) = ∑=p(s)r(s) = 1/ n ∑r(s) The arithmetic average provides an unbiased estimate of the expected future return
equity
Equityholders are not promised any particular payment. They receive any dividends the firm may pay and have prorated ownership in the real assets of the firm. If the firm is successful, the value of equity will increase; if not, it will decrease. More risky than debt securities.
Invoice Price
Flat Price + Accrued Interest
horizon analysis
Forecasting the realized compound yield over various holding periods or investment horizons is called horizon analysis. The forecast of total return depends on your forecasts of both the price of the bond when you sell it at the end of your horizon and the rate at which you are able to reinvest coupon income
federal funds
Funds in the accounts of commercial banks at the Federal Reserve Bank
the risk-free rate for an investment horizon
Given the price, P(T), of a Treasury bond with $100 par value and maturity of T years, we calculate the total risk-free return available for a horizon of T years as the percentage increase in the value of the investment. rf (T) = 100 /P(T) − 1
Difference between YTM and HPR
Here is another way to think about the difference between yield to maturity and holding-period return. Yield to maturity depends only on the bond's coupon, current price, and par value at maturity. All of these values are observable today, so yield to maturity can be easily calculated. Yield to maturity is commonly interpreted as a measure of the average rate of return if the investment in the bond is held until the bond matures. In contrast, holding-period return is the rate of return over a particular investment period and depends on the market price of the bond at the end of that holding period; of course this price is not known today. Because bond prices over the holding period will respond to unanticipated changes in interest rates, holding-period return can at most be forecast.
Bond stripping
If the bond were selling for more than the sum of the values of its individual cash flows, they would run the process in reverse: buy the individual zero-coupon securities in the STRIPS market, offer opportunities for arbitrage—the exploitation of mispricing among two or more securities to clear a riskless economic profit.
exercise price
In stock options trading, the number of shares in a put or call CONTRACT (normally 100) multiplied by the EXERCISE PRICE. The price of the option, called the PREMIUM, is a separate figure not included in the aggregate exercise price. A July call option on 100 XYZ at 70 would, for example, have an aggregate exercise price of 100 (number of shares) times $70 (price per share), or $7,000, if exercised on or before the July expiration date.
Fischer Hypothesis
Irving Fisher (1930) argued that the nominal rate ought to increase one-for-one with expected inflation, E(i). The so-called Fisher hypothesis is rnom = rreal + E(i)
Secondary market
Later, investors can trade previously issued securities among themselves in the so-called
Primary market
Ultimately, the investment banking firm handles the marketing of the security in the primary market, where new issues of securities are offered to the public.
Tax advantage on Preferred stock
When one corporation buys the preferred stock of another corporation, it pays taxes on only 30% of the dividends received. For example, if the firm's tax bracket is 35%, and it receives $10,000 in preferred-dividend payments, it will pay taxes on only $3,000 of that income: Total taxes owed on the income will be .35 × $3,000 = $1,050. The firm's effective tax rate on preferred dividends is therefore only .30 × 35% = 10.5%. Given this tax rule, it is not surprising that most preferred stock is held by corporations
Par value
When the bond matures, the issuer repays the debt by paying the bond's par value (equivalently, its face value).
lognormal distribution
While the probability distribution in Figure 5.9 is bell-shaped, it is a distinctly "asymmetric bell" with a positive skew, and the distribution is clearly not normal. In fact, the actual distribution approaches the lognormal distribution. "Lognormal" means that the log of the final portfolio value, ln(WT) is normally distributed.
realized compound return
With a reinvestment rate equal to the 10% yield to maturity, the realized compound return equals yield to maturity. But what if the reinvestment rate is not 10%? If the coupon can be invested at more than 10%, funds will grow to more than $1,210, and the realized compound return will exceed 10%. If the reinvestment rate is less than 10%, so will be the realized compound return.
normal distribution
a bell-shaped curve, describing the spread of a characteristic throughout a population
Callable bond
a bond that the issuer has the right to pay off before its maturity date. Typically come with a period of call protection, an initial time during which the bonds are not callable. Such bonds are referred to as deferred callable bonds.
Variance
a measure of volatility. It measures the dispersion of possible outcomes around the expected value. Volatility is reflected in deviations of actual returns from the mean return. σ2 = ∑p(s)[r(s) − E(r)]^2
Systemic risk
a potential breakdown of the financial system when problems in one market spill over and disrupt others.
commercial paper
a written promise from one company to another to pay a specific amount of money. Backed by a bank line of credit, which gives the borrower access to cash that can be used (if needed) to pay off the paper at maturity
junk bond
also known as high-yield bonds, are nothing more than speculative-grade (low-rated or unrated) bonds
banker's acceptance
an order to a bank by a customer to pay a sum of money at a future date
Financial assets
are claims to the income generated by real assets (or claims on income from the government).
municipal bonds
are issued by state and local governments. They are similar to Treasury and corporate bonds except that their interest income is exempt from federal income taxation.
Zero-coupon bonds
are issued that make no coupon payments. In this case, investors receive par value at the maturity date but receive no interest payments until then: The bond has a coupon rate of zero. These bonds are issued at prices considerably below par value, and the investor's return comes solely from the difference between the issue price and the payment of par value at maturity
futures contract
calls for delivery of an asset (or in some cases, its cash value) at a specified delivery or maturity date for an agreed-upon price, called the futures price, to be paid at contract maturity. The long position is held by the trader who commits to purchasing the asset on the delivery date. The trader who takes the short position commits to delivering the asset at contract maturity.
Passive management
calls for holding highly diversified portfolios without spending effort or other resources attempting to improve investment performance through security analysis
liquidity premium
compensates short-term investors for the uncertainty about the price at which they will be able to sell their long-term bonds at the end of the year
kurtosis
concerns the likelihood of extreme values on either side of the mean at the expense of a smaller likelihood of moderate deviations. Average[ (R − ¯ R ) ^4/σ ^ 4 ] − 3
Asset allocation
decision is the choice among these broad asset classes
effective annual rate (ear)
defined as the percentage increase in funds invested over a 1-year horizon. For a 1-year investment, the EAR equals the total return, rf (1), and the gross return, (1 + EAR), is the terminal value of a $1 investment. For investments that last less than 1 year, we compound the per-period return for a full year. For investments longer than a year, the convention is to express the EAR as the annual rate that would compound to the same value as the actual investment. 1 + EAR = [1 + rf (T)] 1/T
event tree
depicts all possible sequences of events
derivative assets
derive their values from the values of other assets. These assets are also called contingent claims because their payoffs are contingent on the value of other values.
Collateralized Debt Obligation (CDO)
emerged in the last decade as a major mechanism to reallocate credit risk in the fixed-income markets. To create a CDO, a financial institution, commonly a bank, first would establish a legally distinct entity to buy and later resell a portfolio of bonds or other loans.
short rate
for a given time interval (e.g., one year) refers to the interest rate for that interval available at different points in time.
Convertible bond
give bondholders an option to exchange each bond for a specified number of shares of common stock of the firm. The conversion ratio is the number of shares for which each bond may be exchanged.
call option
gives its holder the right to purchase an asset for a specified price, called the exercise or strike price, on or before a specified expiration date.
put option
gives its holder the right to sell an asset for a specified exercise price on or before a specified expiration date.
Put bond
gives this option to the bondholder. If the bond's coupon rate exceeds current market yields, for instance, the bondholder will choose to extend the bond's life. If the bond's coupon rate is too low, it will be optimal not to extend; in this case, the bondholder will instead reclaim principal, which can be invested at current yields.
preferred stock
has features similar to both equity and debt. Like a bond, it promises to pay to its holder a fixed amount of income each year
Financial intermediaries
have evolved to bring the suppliers of capital (investors) together with the demanders of capital (primarily corporations and the federal government).
Risk-return trade off
higher-risk assets priced to offer higher expected returns than lower-risk assets
collateral
is a particular asset that the bondholders receive if the firm defaults on the bond. If the collateral is property, the bond is called a mortgage bond. If the collateral takes the form of other securities held by the firm, the bond is a collateral trust bond. In the case of equipment, the bond is known as an equipment obligation bond
Bond
is a security that is issued in connection with a borrowing arrangement. The borrower issues (i.e., sells) a bond to the lender for some amount of cash; the bond is the "IOU" of the borrower. The arrangement obligates the issuer to make specified payments to the bondholder on specified dates
Money market
is a subsector of the fixed-income market. It consists of very shortterm debt securities that usually are highly marketable
yield-to-maturity (YTM)
is defined as the interest rate that makes the present value of a bond's payments equal to its price.
bid-ask spread
is the difference in these prices, which is the dealer's source of profit.
Conversion premium
is the excess of the bond's value over its conversion value. If the bond were selling currently for $950, its premium would be $150.
Value at Risk (VaR)
is the loss corresponding to a very low percentile of the entire return distribution, for example, the 5th or 1st percentile return. VaR(1%, normal) = Mean − 2.33SD
ask price
is the price you would have to pay to buy a T-bill from a securities dealer.
London Interbank Offered Rate (LIBOR)
is the rate at which large banks in London are willing to lend money among themselves
price-earnings ratio
is the ratio of the current stock price to last year's earnings per share. The P/E ratio tells us how much stock purchasers must pay per dollar of earnings that the firm generates
bid price
is the slightly lower price you would receive if you wanted to sell a bill to a dealer.
credit default swap (CDs)
is, in effect, an insurance policy on the default risk of a bond or loan. The CDS seller collects annual payments for the term of the contract but must compensate the buyer for loss of bond value in the event of a default
floating-rate bonds
make interest payments that are tied to some measure of current market rates. For example, the rate might be adjusted annually to the current T-bill rate plus 2%. If the 1-year T-bill rate at the adjustment date is 4%, the bond's coupon rate over the next year would then be 6%. This arrangement means that the bond always pays approximately current market rates
Capital market
market in which money is lent for periods longer than a year
residual claim
means that stockholders are the last in line of all those who have a claim on the assets and income of the corporation.
limited liability
means that the most shareholders can lose in the event of failure of the corporation is their original investment.
Venture capital
money invested to finance a new firm. Sources of venture capital are dedicated venture capital funds, wealthy individuals known as angel investors, and institutions such as pension funds.
current yield
of a bond, which is the bond's annual coupon payment divided by the bond price. For example, for the 8%, 30-year bond currently selling at $1,276.76, the current yield would be $80/$1,276.76 = .0627, or 6.27%, per year.
Coupon Rate
of the bond determines the interest payment: The annual payment is the coupon rate times the bond's par value.
certificate of deposit
or CD, is a time deposit with a bank. Time deposits may not be withdrawn on demand. The bank pays interest and principal to the depositor only at the end of the fixed term of the CD
fixed-income (debt) securities
pay a specified cash flow over a specific period
Investment bankers
pecialize in such activities can offer their services at a cost below that of maintaining an in-house security issuance division. In this role, they are called underwriters
Real assets
physical property like gold, machinery, equipment, or real estate
pure yield curve
refers to the curve for stripped, or zero-coupon, Treasuries.
On-the-run yield curve
refers to the plot of yield as a function of maturity for recently issued coupon bonds selling at or near par value
yield to maturity
reported in the last column is calculated by determining the semiannual yield and then doubling it, rather than compounding it for two half-year periods.
equities
represent ownership shares in a corporation. Each share of common stock entitles its owner to one vote on any matters of corporate governance that are put to a vote at the corporation's annual meeting and to a share in the financial benefits of ownership
Market conversion value
s the current value of the shares for which the bonds may be exchanged. At the $20 stock price, for example, the bond's conversion value is $800.
repurchase agreements
short-term sales of government securities with an agreement to repurchase the securities at a higher price
Derivative securities
such as options and futures contracts provide payoffs that are determined by the prices of other assets such as bond or stock prices
price-weighted average
the Dow corresponds to a portfolio that holds one share of each component stock, the investment in each company in that portfolio is proportional to the company's share price. Therefore, the Dow is called a
Active management
the attempt to improve performance either by identifying mispriced securities or by timing the performance of broad asset classes
Security selection
the choice of which particular securities to hold within each asset class
Investment
the current commitment of money or other resources in the expectation of reaping future benefits
risk premium
the excess return required from an investment in a risky asset over that required from a risk-free investment
Real interest rate
the growth rate of your purchasing power
Agency problem
the possibility of conflict of interest between the stockholders and management of a firm
bond reconstitution
the process in reverse: buy the individual zero-coupon securities in the STRIPS market, reconstitute (i.e., reassemble) the cash flows into a coupon bond, and sell the whole bond for more than the cost of the pieces.
Holding-period returns
the rate of return earned on an investment, which equals the dollar gain divided by the amount invested. HPR = (Ending price of a share − Beginning price + Cash dividend)/Beginning price
risk-free rate
the rate you would earn in risk-free assets such as T-bills, money market funds, or the bank.
reinvestment rate risk
the risk that a decline in interest rates will lead to lower income when bonds mature and funds are reinvested. This reinvestment rate risk will offset the impact of price risk.
credit risk
the risk that borrowers might default on their loans
term structure of interest rates
the structure of interest rates for discounting cash flows of different maturities
Liquidity Preference Theory
the theory that investors demand a risk premium on long-term bonds. Of the term structure believe that short-term investors dominate the market so that the forward rate will generally exceed the expected short rate. The excess of f2 over E(r2), the liquidity premium, is predicted to be positive.
debenture bond
which are unsecured, meaning they do not provide for specific collateral. Credit risk of unsecured bonds depends on the general earning power of the firm. If the firm defaults, debenture owners become general creditors of the firm. Because they are safer, collateralized bonds generally offer lower yields than general debentures
Yield curve
which is a plot of yield to maturity as a function of time to maturity. The yield curve is one of the key concerns of fixed-income investors. It is central to bond valuation and, as well, allows investors to gauge their expectations for future interest rates against those of the market.
Investment companies
which pool and manage the money of many investors, also arise out of economies of scale
index funds
yield a return equal to that of the index and so provide a low-cost passive investment strategy for equity investors.
sortino ratio
Practitioners who replace standard deviation with this LPSD typically also replace the Sharpe ratio (the ratio of average excess return to standard deviation) with the ratio of average excess returns to LPSD. This variant on the Sharpe ratio is called the
Sharpe Ratio
Reward-to-volatility ratio; ratio of portfolio excess return to standard deviation. Sharpe ratio = Risk Premium/STDEV of excess return
Bond Indenture
The coupon rate, maturity date, and par value of the bond are part of the bond indenture, which is the contract between the issuer and the bondholder
risk aversion
The degree to which investors are willing to commit funds to stocks depends on their risk aversion. Investors are risk averse in the sense that, if the risk premium were zero, they would not invest any money in stocks. In theory, there must always be a positive risk premium on stocks in order to induce risk-averse investors to hold the existing supply of stocks instead of placing all their money in risk-free assets.
excess return
The difference in any particular period between the actual rate of return on a risky asset and the actual riskfree rate is called the
Real Return
(1 + Nominal return/1 + Inflation) - 1
forward interest rate
(1 + yn) n = (1 + yn−1) n−1 × (1 + rn ) (1 + rn ) = (1 + yn ) n / (1 + yn−1) n−1 Recognizing that future interest rates are uncertain, we call the interest rate that we infer in this matter the forward interest rate rather than the future short rate because it need not be the interest rate that actually will prevail at the future date. (1 + yn ) n = (1 + yn−1) n−1 (1 + fn)
Nominal Return
(Interest + price appreciation) / initial price
premium bonds
(bonds selling above par value), coupon rate is greater than current yield, which in turn is greater than yield to maturity
discount bond
(bonds selling below par value), these relationships are reversed
Nominal interest rate
The growth rate of your money
expectations hypothesis
The hypothesis maintains that the yields on long-term securities are a function of short-term rates. The result of the hypothesis is that, when long-term rates are much higher than short-term rates, the market is saying that it expects short-term rates to rise. Conversely, when long-term rates are lower than short-term rates, the market is expecting short-term rates to fall.
expected shortfall (es)
-Also called conditional tail expectation (CTE) -Focuses on the *expected loss* in the worst case scenario (left tail of the distribution) -More conservative measure of downside risk than VaR
Formula to find the difference in purchasing power
1 + rreal = 1 + rnom /1 + i A common approximation to this relation is rreal ≈ rnom − i The exact relationship in Equation 5.1 can be rearranged to rreal = rnom − i / 1 + i
Why the yield curve might take on different shapes
1 + y2) 2 = (1 + r1) × (1 + r2) 1 + y2 = [(1 + r1) × (1 + r2)] 1/2
Terminal value
= (1 + r1) × (1 + r2) × . . . × (1 + r5) = 1.0275 (1 + g) n = Terminal value = 1.0275 (cell F6 in Spreadsheet 5.2) (5.14) g = Terminal value1/n − 1 = 1.02751/5 − 1 = .0054 = .54% (cell F14)=
Accrued interest
= annual coupon payment/2 * Days since last coupon payment/days separating coupon payments Suppose that the coupon rate is 8%. Then the annual coupon is $80 and the semiannual coupon payment is $40. Because 30 days have passed since the last coupon payment, the accrued interest on the bond is $40 × (30/182) = $6.59. If the quoted price of the bond is $990, then the invoice price will be $990 + $6.59 = $996.59.
Bond Value
=Present value of coupons + PV of par value =sum(coupon/(1+r)^t + Par value/(1+r)^T
Price bond
=coupon* 1/r[1-1/(1+r)^T] + Par value*1/(1+r)^T =coupon*annuity factor(r, T) + Par Value*PV Factor (r,T)
Debt securities
A debt security is a claim on a specified periodic stream of income. Debt securities are often called fixedincome securities because they promise either a fixed stream of income or one that is determined according to a specified formula.
skew
A measure of asymmetry called skew is the ratio of the average cubed deviations from the sample average, called the third moment, to the cubed standard deviation: Skew = Average[ ((R − ¯ R) ^ 3 ) / σ ^ 3]
conditional tail expectation (CTE)
A more informative view of downside exposure would focus instead on the expected loss given that we find ourselves in one of the worst-case scenarios. This value, unfortunately, has two names: either expected shortfall (ES) or conditional tail expectation (CTE); the latter emphasizes that this expectation is conditioned on being in the left tail of the distribution.
Lower Partial Standard Deviation (LPSD)
A risk measure that addresses these issues is the lower partial standard deviation (LPSD) of excess returns, which is computed like the usual standard deviation, but using only "bad" returns` is therefore the square root of the average squared deviation, conditional on a negative excess return.
dividend yield
The percent return from dividends is called the dividend yield, and so dividend yield plus the rate of capital gains equals HPR.
Face value
Amount of principal due at the maturity date of the bond
Annual Percentage Rate (APR)
Annualized rates on short-term investments (by convention, T < 1 year) often are reported using simple rather than compound interest. 1 + EAR = [1 + rf (T)] ^n = [1 + rf (T)] ^1/T = [1 + T × APR] ^1/T APR = ((1 + EAR)^T) − 1 / T
Continuous compounding (CC)
As T approaches zero, we effectively approach continuous compounding (CC), and the relation of EAR to the annual percentage rate, denoted by rcc for the continuously compounded case, is given by the exponential function 1 + EAR = exp(rcc) = e^rcc where e is approximately 2.71828 ln(1 + EAR) = rcc
Real after-tax rate
The real after-tax rate is approximately the after-tax nominal rate minus the inflation rate: rnom(1 − t) − i = (rreal + i)(1 − t) − i = rreal(1 − t) − it
treasury bonds
Bonds issued by the federal government, sometimes referred to as government bonds. is the rate at which large banks in London are willing to lend money among themselves
