Exam 2 Review Chapter 5 1 Rates of Return a Holding Period Return rate of return over a given investment period i When dividends are received earlier ignore reinvestment income between receipt of dividend and end of holding period ii Percentage return from dividends cash dividends beginning price is dividend yield and dividend yield plus capital gains yield equal HPR b Arithmetic Average Sum of returns in each period divided by the number of periods i Ignores compounding so does not represent an equivalent single quarterly rate for the year ii Best forecast of performance for the next quarter c Geometric Average the single per period return that gives the same cumulative performance as the sequence of actual returns i Also called the time weighted average return ignores the quarter to quarter variation under management ii Required to publish for mutual funds 2 Risk and Risk Premiums a Scenario Analysis process of devising a list of possible economic scenarios and specifying the likelihood of each one as well as the HPR that will be realized in each case i Probability Distribution is the list of possible outcomes with associated ii The reward of the investment is the expected return the average HPR you would earn if you were to repeat an investment in the asset many times iii Expected return is also the mean of the distribution of HPRs and often called the probabilities mean return iv Scenarios s HPR r s Probability p s Expected Return E r v The surprise return in any scenario is the difference between actual return and the expected return vi To summarize risks we define variance as expected value of the squared deviation from the mean the expected squared surprise across scenarios i The standardized return is normally distributed with a mean of zero and standard deviation of 1 sr is a standard normal variable ii Simplify analysis of risk applies to daily and monthly returns applies well to continuously compounded returns iii Two things to note 1 Return on a portfolio of two or more assets whose returns are normally distributed also will be normally distributed 2 Normal distribution is completely described by its mean and standard deviation No other stat is needed to learn about the behavior b Normal Distribution 3 Standard deviation is the appropriate measure of risk for a portfolio of assets with normally distributed returns In this case no other stat can improve the risk assessment conveyed by the SD of a portfolio iv Value at Risk VaR measure the downside risk The worst loss that will be suffered with a given probability often 5 3 Risk Premiums and Risk Aversions a Measure the reward as the difference between expected HPR on the index fund and b the risk free rate rate earned on a T bill this difference is the risk premium In theory there must always be a positive risk premium on all risky assets in order to induce risk averse investors to hold the existing supply of assets c Risk premium and the level of risk that can be attributed to individual assets in the complete wealth portfolio are of no concern to the investor all that counts is the complete portfolio complete portfolio risk premium versus complete portfolio risk d Price of risk the ratio of portfolio risk premium to variance e Conventional wisdom estimates for the value of A risk aversion to lie in the range of 1 5 4 portfolio 4 Sharpe reward to Volatility Ratio ratio of portfolio risk premium to standard deviation a A higher Sharpe ratio indicates a better reward per unit of volatility a more efficient b A portfolio analysis in terms of mean and standard deviation of excess returns is called mean variance analysis Sharpe ratio is a valid stat only for ranking portfolios not for individual assets c 5 Asset Allocation across risky and risk free portfolios a Asset allocation is the portfolio choice among broad investment classes b The fraction of a portfolio placed in risky assets is called capital allocation to risky assets c The complete portfolio is the entire portfolio including risky and risk free assets 6 Risk Free Asset free bonds a The power to take and to control the money supply lets the government issue default b Money market mutual funds hold three types of securities t bills bank certificates of deposits and commercial paper c We treat money market funds and t bills as the most easily accessible risk free asset for most investors 7 Portfolio Expected Return and Risk a We assume the composition of the risky portfolio P is already determined and the proportion of the investment budget w to be allocated to it b The remaining 1 w is the risk free asset rate of return denoted rf c Denote the actual risky rate of return by rp the expected rate of return on P by E rp d Expected Return w E rp 1 w rf rp and rf are the means of risk free and risky e SD w SD of risky 8 Capital Allocation Line plot of risk return combinations available by varying portfolio allocation between a risk free asset and a risky portfolio a The slope equals the increase in expected return that an investor can obtain per unit of additional standard deviation or extra return per extra risk Intercept is the risk free rate b c The reward to volatility ratio is the same for all complete portfolios that plot on the CAL 9 Risk Aversion and Capital Allocation a The compensation for risk demanded by the investor must be compared to the price of risk offered by the risky portfolio P b We find the investor s preferred capital allocation by dividing the risky portfolio s price of risk by the investor s risk aversion her required price of risk c When the price of risk of the available risky portfolio exactly matches the investor s degree of risk aversion her entire wealth will be invested in it w 1 10 Passive Strategies and Capital Market Line a Passive strategy is based on the premise that securities are fairly priced and avoid costs undertaking security analysis b Capital Market Line is the allocation line using market index portfolio as the risky asset Homework Questions You invest 1 000 in a complete portfolio The complete portfolio is composed of a risky asset with an expected rate of return of 16 and a standard deviation of 20 and a Treasury bill with a rate of return of 6 The slope of the capital allocation line formed with the risky asset and the risk free asset is approximately 1 040 80 50 25 18 88 9 7 11 8 42 Slope 16 6 20 50 The geometric average of 12 20 and 25 is 1 12 1 20 1 25 1 3 1 9 70 The reward to volatility ratio is given by the slope