Study Session 12

Portfolio perspective refers to evaluating individual investments by their contribution to risk and return of an investor's porftolio. Alternative is to examine risk and return of individual investments in isolation.

One measure of benefits of diversification is the DIVERSIFICATION Ratio. ratio of risk of an equally weighted profolio of N securities (measured by standard deviation of returns) to risk of a single security selected at random from n securities.

If avg standard deviation fo returns for n stocks is 25% and standard devaiton of returns for equally porftolio of n stock is 18% diversification ratio is 18/25.

Equally weighted proftolio does not necessarily provide greatest reduction in risk. Computer optimizatioon can caluclulate this, which produces lowest pstandard deviation of returns for given securities.

Portfolio diversification works bset when financial markets are operating normally. During financial crisis, correlations tend to increase, and lessens benefits of diviersifcation.

• Individuals - all depends
• DB Pensions - High, Long, Low, Depends on age
• Banks - Low, Short, High, Pay Interest
• Endowments - High, Long,Low, Spending
• Insurance - Low, depends(life-long)(Property&Casulaty-Short), High, Low
• Mutual Funds - Depends, Depends, High, Depends.

• 1. Planning Step - investors risk tolerance , return objectives, time horizon, tax exposure, liquidity needs, income needs, unique circumstance. (RRLLTTU Risk, Return, Liquidity, Legal, Tax, Time, Unique Circumstances.)
• Should spevcify benchmarg against which sucess wis measured. Should be updated every few years.

2.Execution step involves analysis of risk and return characteristics. Two strategies are Top Down (Examin current economicn condidtions and forecasts of macroeconomic variables and identify asset classes most attractive) and Bottom up (ID undervalued securites.

Step 3 feedback step investors changing circumstances and weights of assets must be reblaance d in the proftolio.

Mutual fund is pooled investments. Each investor owns a share repersent ing ownerhsip of overall portfolio. Net Asset value is porfolio assets in fund divided by number of shares issued.

Open end fund is when you can buy newly issued shares at the NAV. Investors can also redeem their shares at NAV as well. Can have load which is fee charged at begining, end or never.

Closed fund is a managed pool of money that doesnt' take on new invesmtnets. can trade at price that varies from NAV.

Money Market fund- invest in short term debt secrutiies and provide interest income with low risk of change in share value. NAV are one to one currency unit.

Bond mutual fund invest in fixed in come securites

Stock mtuual fund are in stocks.

Index funds are passivley amnaged.

ETF trade as shares like close end, but have a redeemable feature that allow you to keep market price very close to NAV.

ETFs can also be sold short, but pay brokerage, and spread, and receive dividencd income, while open end funds offer alternative to reinvestin dividends in additional fund shares. ETFs produce less capital gains liability.

• Find time periods of when money flows in and out of account.
• T=0+80 Inflow to account
• T=1 +70-1.50=68.5
• T=2 -170-3.00=-173

CF0=80 CF1=68.5 CF2=-173 Compute IRR.

If we use less than one year, say one month per period(zero cash flow for months with no cash flow), internal rate of return calculation will yiled a montly rate of return. IN that case we would need to compoun the monthly weighted return for 12 monmths to translate it into an effective annual rate.

Gross return is total return on secruitey portfolio before deducting fees for mgmt and admin of investment account.

Net return refers to return after fees have been deducted.commisions on trade are necessary to gerneate invement return and are deducted in both gross and net.

After tax nominal return - return after tax is deducted

Real Return is return/inflation. Inflation is 2% real return is 7, 1.07/1.02.

Leveraged reutns is calculated as gain or loss on investment as percentag of investors cash invesmtnet.

(X1-mean)^2+(X2-mean)^2...../N

if it is sampel N-1

to get standard deviation we take squar root.

(Return A in period 1-Mean return)*(Return B in period 1-Mean Return)+...../n-1

Correlation = Covariance/Standard deviation A*Standard Devaiton B

Wweight A^2*Variance A+Weight B^2*Varaince B+2*Standard DevA * Standard Dev B*Correlation*Weight A*Wight of B.

Square root of everything gets porftolio Standard Dev.

The correlation * Dev A*Dev B can be stubtitiuted for covariance.

If correlation is 1 Variance = Weight A*Stdv A+Weight B*StdvB.

If correlation is 0 = Weight A^2*Stdv A+Weight B^2*StdvB.

Note that proftolio risk falls as correlation btwn assets return decreass. Lower correlation of asset return, greater risk reduction (diversification).If asset returns are perfectley negativley correlated, portolio risk could be elimanted altogether FOR A SPECIFIC SET OF ASSET WEIGHTS. Does not mean 50/50 split.

minimum variance is portfolio that has lowest standard deviation of all porftolios with a given expected return. Efficient frontier are portfolios that have lowest amount of risk for a given return. Any investor would ideally want a portfolio that is on this. The furthest to the left porftolio on the efficient frontier line which looks liek a C, with bottom half gone, bc this is a portolio with lowest amount of portfolio risk (portfolio standard devaiation.

Shape is curves up but as X axis is higher, Expected return exponetnially gets greater. More risk avers investers will have steeper indifierence curve, meaning they need more return (Y axis) for risk (x-axis = standard deviation).

To find expected return, you take expected return of portfolio * Weight + Expected return of risk free asset * Weight.

The risk is simply Weight of Risky porftolio*Deviation of portfolio.

Possible portfolio risk and return combos given for risk free rate and risk and return of portfolio of risky assets. As more risky portfolio is included, the deviation and expected return go up.

Assumes investors with same estimates of risk, return and correlations with other risk assets for all risky assets.

• Expected return of portfolio =
• RFR+(ErMarket-RFR)*(Devation of protfolio/Devation of Market)

Non systematic risk can be diversified away.

Equation is Total risk = non systematic+systematic risk

• Non systematic can be diviersified aways
• systemati can't

You do not expect to get paid for risk that can be diviersified away. IF a biotech stock price is primarily dependant on whether a specific drug gets passed by the FDA, the price may not change much if markets are good or bad. Therefore, altho the unsystematic risk is high, and risk is high, the unsystematic risk is lower than a stock that may be more dependant on the market ( say an established producer of amchine tools) which isn't a risky investment but sensitive to market factors (GDP, etc.

Return Gernerating models used to estimate expected return on risky securiteies based on specific factors. 3 groups are macroeconomic, fundamental and statistical. S taical often have nob asis in finance theory.

Mutlifactor mode use macroeconomic and fuandments, not much statistic.

• Market mode, is a singlfe factore.
• Equation would be Market premium (over rfr)= Beta (Er-RFR)

Beta =covaraince of assets return with amrket return/Variance of MARKET Return. Additonally, can be which is same equation, Beta= Correlation *Stadard deviation of Investmetn/Market.

The elast square regression line is line that minimizes sum of squared istance of points plotted from line of best fit. Slope of this is Beta.

.8(.3/.2)=1.2

.048/(.2^2)= 1.2

Know how to calculat e both ways

SML line is E(R)=RFR+Beta(ERmkt-RFR) Beta is Covariance of market and secrutiy/Variance of market

SML is CAPM.CAPM holds that, in equilibrium, expected return on risky asset is the risk free rate plus a beta adjusted market risk premium which is beta *(mkt-RFR). BETA MEASURES SYSTEMATIC RISK.

SML is CAPM, ideally all portfolios should be on this line. Return vs. variance from market.

CML is line of portfolio and Risk free securityweights, and isp lotted with the Efficient frontier. Return vs risk of portfolio rteruns. Portoflios not well diversified plot inside efficient frontier line. Individual securites examples of this.

CAPM expected return on all protfolios, well divierisifed or not are determined by their systematic risk.

All po ints on CML except for tangency point with efficient frotniers, are formed by either combinding market profolio with risk free asset, or borring at risk free rate in order to invest more tahn 100% Net value of portfolios value in the risky market. Portfolios not lying on CML ARE NOT EFFICIENT and have risk that will not be rewarede with higher expected returns in market equilibrium.

If forecasted return is greater, you buy the stock. If Expected is less than requried, you short sell. If matching, you buy sell or ignore.

Bc sharep ratio accounts for unsystematic risk, look at equation, is useful when comparing sharpe ratio to another sharpe ratio.

M Squared measure produces same protfolio ranking as sharpe ratio bust staed in percentage term.Calculated at RP-RFR(STDVM/STDVP)-(RP-RFR). Look at pg 185 to show this.

Mesaures a portfolios excess return per unit of systematic risk. Jensne's alpsh is the deference between a porfolios retrun and return of a portfolio of the SML that has same beta.

Treyno = Rp-Rf/BetaP

Jensesns alpha = Rp - RF+Betap(Rm-RFR)