Foundations of Finance

Beta

Definition of the slope of a regression line Cov(Ri,Rm)/SD^2m Measures the security's sensitivity to market movements Stock i's systemic or market risk

What determines what type of market will emerge for a given asset?

Determined by how standardized an asset is and volume of trade

Security market line

E(Ri)=Rf+Beta*E(Rm-Rf)

Geometric average

Takes compounding into account Gives the equivalent per period return (Accumulated valueT/Value0)^(1/T)-1

Arbitrage

The ability to make a profit without having cash outplayed by yourself Zero risk, zero net investment strategy that still generates profits

Treasuries (3 types)

Treasury bills (less than one year maturity) Treasury notes (1-10 year maturity) Treasury bonds (10-30 year maturity) Semi annual coupon payments Pays 5% interest

Insurance principle

If add lots of uncorrelated assets, the risk is diversified away

Annual holding period return

((V(T)/V(0))^(1/T) - 1 Takes time into account

Variance

(Return of state-ave)^2 * prob of that state Measure of the dispersion or variability if the outcomes around its mean

Annual return

(V'/V)^(1/T)-1 V' = value at the end V= value at beginning

Liquidity

Ability to trade an asset IMMEDIATELY close to the true price (without a big impact in price)

Two features of portfolio weights

-sum to 1 -negative weight equals a short position

Beta of risk free asset

0 because covariant of risk free asset is 0

Beta of market portfolio

1

Three sources of risk

1) Economy wide 2) Industry specific 3) Firm specific

Finance is based on four axioms

1) investors prefer more to less 2) Investors are risk averse 3) money paid in the future is worth less than the same amount today 4) financial markets are competitive; no arbitrage

Use of financial assets

1. Allocation/raising of capital (shift capital from people who have it to people with the best uses for it) 2. Allocation of risk (diversification) - risk sharing 3. Consumption smoothing

Discount factor (present value factor)

1/(1+R)^T

US GDP and debt as share of GDP

17 trillion and 105%

Corporate bonds

4.5 trillion (non financial) Default risk - become very worried about this Commercial paper - borrow short term (90 days) Corporate bonds (longer term, typically semi annual payments, different seniority classes, including senior and junior)

Asset allocation makes up what percent of portfolio performance

94%

Random Variable

A variable whose value depends uniquely on the outcome of an experiment

Zero coupon bond sold after t' years (with t' less than maturity) at a price of P'

Ann return = (P'/P)^(1/t')-1 This R is YTM but also Ann. HPR if you hold the bond until maturity

Volatility

Another word for standard deviation

Three measures of multi period realized return

Arithmetic average Geometric average IRR

Real assets

Assets used to produce goods and services 50 trillion in US

Yield to maturity for a bond

At what rate does $PV grow up to $FV in a span of T years R=(FV/PV)^(1/T)-1

Covariance between two random variables

Average of the products of their deviations from the mean Measures the comovement of two random variables

Asset backed securities

Bundling of existing securities such as mortgages, auto loans, corporate bonds

Stop buy order

Buy when it hits price

Most risk less asset

Cash - still has inflation risk

Online brokers

Charles Schwab, e-trade

Financial assets

Claims on real assets (stocks and bonds) Derivatives (contingent claims)

Feasible

Combinations of assets: principles of diversification -Investment opportunity set -Efficient frontier

How many classes of equities

Common stock: voting rights (junior) Preferred stock: non-voting but more senior when bankruptcy

Investment opportunity set

Consists of all available risk-return combinations

Maximal gains from diversification

Correlation =-1

True cost of credit

Effective annual rate If interest is compounded m times a year EAR= (1+quoted rate / m)^m - 1 Quoted rate = APR

Equilibrium expected return on security i

Equals risk free rate + market price of risk * risk contribution of security i to portfolio risk SDm

CAPM (Capital Asset Pricing Model)

Equilibrium model that: Predicts the relationship between risk and expected return Underlies much of real world financial decision making

All wealth in he economy is real

Every financial security is an asset for somebody and a liability for somebody else

Securitization

Example of financial engineering

Continuous compounding EAR

Exp(quoted rate) - 1 e^ on calc

The risk free return is known for sure

Expected return = R(f) Standard deviation = 0 Correlation is 0 for any other asset

Trading costs

Explicit cost: commission Implicit cost: bid-ask spread or for large investors, market impact

FV - investing for multiple periods (T periods) - compounding

FV = PV (1+R)^T

FV - investing for a single period

FV=PV(1+R)

FV - investing for multiple periods (T periods) - simple interest

FV=PV(1+R*T)

Mutual funds

Financial intermediaries that pool funds from investors and buy assets (active management) Need to pay a high fee

Fixed income securities

Fixed cash flows - coupons or interest payments (interest that is paid is fixed up front) Examples: borrowing instruments and bonds (treasury, municipal, corporate) Valuation: time value of money adjustment

Single payment security - zero coupon bond

Fixed income that pays face value at maturity but no intermediate interest payments Lower interest rates = higher bond prices

Government securities vs corporate securities

Government securities are auctioned, corporate securities are underwritten by investment banks

Ask bid spread changes

Higher volume of trade leads to lower bid ask spread Higher equilibrium price volatility increases bid ask spreads More competition among dealers leads to lower bid ask spread

Present value - single period case

How much do you need to invest today, with an interest rate of R, to have $FV next year PV=FV*1/(1+R)

Market order

I want buy no matter the price

Limit order

I want to buy but there is a limit I am willing to pay

No gains from diversification

If correlation equals 1

Covariance is negative

If he one variable tends to be high when the other is low Airline and Oil company

Monetary policy

If rate is lower, banks will be willing to lend at lower rates to households and firms. Households will consumer more and firms will invest more, reducing unemployment As people want to buy more things, the price of things goes up (and inflation increases)

Covariance is positive

If the random variables tend to be high at the same time Apple and Google

When is R=YTM= Ann. HPR for 10 year bond

If you hold the bold until maturity; otherwise interest rates move around, moving the price of bonds

Key risks for treasuries

Interest rate risk and default risk

Secondary markets

Investors usually deal through brokers Broker guarantees counterparty that: -an investor can pay for the security he is buying -an investor can deliver a security he is selling

Municipal bonds

Issued by state and local governments (3.7 trillion) Exempt from federal income tax and state local tax

Revenue bond

Issued to finance specific projects (riskier)

Risk free returns - treasury bills

Less than 1 year

Broker trades

Limit order Market order Stop loss order

Provision of liquidity

Market orders use up liquidity and limit orders provide liquidity because they give a price and quantity at which you can. Up or sell immediately

In equilibrium what has the highest sharpe ratio?

Market portfolio - most return per unit of risk Why? Because it maximizes gains from diversification

Investors optimally trade off risk and return to

Maximize their expected utility

Sharp ratio

Measure risk adjusted performance E[Ri-Rf]/SD Calculated by subtracting the risk free rate rate of return for a risky asset and dividing he result by the standard deviation of risky returns Return per unit of risk

Future value

Measures the nominal future sum of money that a given sum of money today is "worth" at a specified time in the future assuming a certain rate of return

Exchange traded funds (ETF)

Mostly passive and competition of mutual funds

General obligation bond (municipal)

Municipal bond backed by the full faith of credit of the issuer (taxing power) Pays 4% interest

Dealer markets

NASDAQ Trade with dealers who hold inventory i.e. Car dealerships Quote bid and ask (how much you will have to pay the market maker) Price of liquidity service: bid ask spread Asker maker provides immediacy, liquidity Increased standardization Modest volume of trade Reduced effort of search

If beta is greater than 1

Needs to have an expected return greater than the market

Are variance or volatility of individual assets indicator of riskiness?

No - only thing that matters is covariance with other assets

Objectives and instruments of the Fed

Objectives: full employment and stable prices Instrument: interest rate

Equity

Ownership in a firm Future cash flows (dividends are uncertain) Maturity is indefinite Involves risk, variable liquidity Valuation: TVM + risk adjustment

Annuity

PV = C/(1+R)+C/(1+R)^2 ... + C/(1+R)^T PV = C ( (1-1/(1+R)^T ) / R) Pays a fixed cash flow C for T periods

Present value (multiple period case)

PV=FV*1/(1+R)^T

Perpetuity

Pays a fixed cash flow, C, for every period forever PV=C/R

Continuous compounding formula

Pe^(rt)=F Present

Financial markets

Platform on which financial assets are traded

Efficient portfolio

Portfolio that has the highest possible expected return for a given standard deviation

Minimum variance portfolio

Portfolio that provides the lowest variance (standard deviation) among all possible portfolios of risky assets

Desirable

Preferences over risk-return tradeoffs

Pricing of single payment securities (zero coupon bond)

Price = PV = FV / (1+R)^T

Pricing of securities

Price =PV by arbitrage

CAPM extra return

Proportional to the risk contribution of the security to the overall market

Capital allocation line

R(f) + (Sharp ratio of i)SD E(Rp)=Rf+E(Rm-Rf)/(SDm)*SD

Federal funds rate

Rate at which banks can borrow from the Fed

Quantitative easing

Rather than reduce the cost of borrowing of banks and hope that they will reduce the borrowing cost of households and firms, the central bank will lend more directly. Buying back mortgage backed securities - if banks know Fed will buy them, will be more likely to make mortgage loans

Annual Percentage Rate (APR)

Required by law Quoted rate Interest per period * number of periods per year Does not take compounding into account

Internal rate of return (IRR)

Return if one is to reinvest cash flows at this rate Discount rate which makes the net present value (PV) of a series of cash flows equal to zero Initial price = present value of future cash flows

One risk free and one risky asset

Return: R(f) + w*E[Ri-Rf] Variance of portfolio = w^2*SD^2 Standard deviation |w|SD

Efficiency frontier for two risky and one risk free asset

Rf , MVE (mean variance efficient), where MVE is the tangency portfolio of the old efficient frontier and the straight line through Rf with the highest sharpe rati

Single index model

Ri=alpha+betaRm+ei

Capital market line

Risk return combinations achieved by forming portfolios from the risk free security and market portfolio

Derivatives

Securities whose cash flow depends on the value of other assets Options, futures, swaps, bonds with option feature Valuation: TVM+risk+option adjustment

Stop-loss order

Sell when it drops below $X

Short sales

Selling shares of a firm not owned by borrowing a security and later replacing it (cover it) Profit is made in the short position is covered at the price lower than the one at which it was established First you sell and then you buy the stock

Efficient frontier

Set of efficient portfolios. It is the upper portion of the minimum variance frontier starting st the minimum variance portfolio

Price of risk

Sharp ratio of market

What portfolio should an investor choose?

Should choose an efficient portfolio but which is optimal depends on risk aversion

Standard deviation

Square root of the variance

Exchange

Standardized assets High volume of trade Central location for buyers and sellers to meet, aggregates supply and demand in one place

Classifications of risk

Systemic risk - can not be diversified away Idiosyncratic risk - can be diversified away

Correlation

The covariance between two random variables, decided by their standard deviations Measures the same co movement as covariance, but has the property that it is unit free. Always between -1 and 1

Pull to par

The increase in value as the bond approaches maturity

Probability distribution

The likelihood of each possible event

How do brokers trade?

Traditional floor trading and electronic trading (NYSE) -marched by Designated Market Makers (DMM) (no inventory) Dealer Markets (Nasdaq) Dealers (market makers) Electronic communication networks - direct trade among investors

Diversification - two risky securities

Truly a free lunch Less risk than either one Higher return than the lower-return security Gains of diversification depend on the degree of correlation between the asset returns Even a positive correlation helps to reduce risk of a portfolio

Primary markets for equity

Typically best effort Book building Road show Filing for an IPO (register with SEC, S-1 filing, approved: prospectus)

Mean variance utility

U(Rp)=E(Rp)-0.5AVar(Rp)

Holding period return

V(T)/V(0)-1 Doesn't take time into account

Portfolio variance

Var [Rp] = w1^2SD^2 + w2^2SD^2+2w1w2(corr)(SD1)(SD2)

Risk in equally weighted portfolios

Variance of portfolio return = average covariance of returns as N goes to infinity No diversifiable risk

Holding period yield

When a bond is sold prior to maturity (annual return)

Primary markets

Where sold to first investors Raises capital How securities are floated (sold)

Yield to maturity

YTM = (F/P)^(1/t)-1 T years to maturity Annual compounding F = face amount P = price

Do longer maturity zeros have greater percentage price volatility than shorter zeros for the same change in interest rates?

Yes