# Return, Risk, and SML Part II Portfolio Portfolio

Return, Risk, and SML Part II Portfolio Portfolio = Collection of individual assets Weight of individual assets in the portfolio Total \$ invested on portfolio = Sum of \$ invested on all individual assets in the portfolio = The fraction of portfolio invested on each individual asset Return, Risk, and SML 2 If we invest on A and B If we invest \$200 on stock A and invest \$800 on B, what is the portfolio weight of on two stocks? Expected return of stocks A is 0.25 and that of B is 0.20, what is the portfolios expected return?

Return, Risk, and SML 3 Example 1) What are the portfolio weights for a portfolio that has 150 shares of Stock A that sell for \$87 per share and 125 shares of Stock B that sell for \$94 per share? Return, Risk, and SML 4 Portfolio Expected Return Weight of stock Expected return of stock Return, Risk, and SML

5 Example 2) Portfolio Expected Return Suppose we had following investments: Security Amount Invested Expected Return Stock A 1,000 8% Stock B 2,000

12% Stock C 3,000 15% Stock D 4,000 18% What is the expected return of this portfolio? Return, Risk, and SML 6

Solution #2) Amount Expected Security Invested Return Stock A 1,000 8% Stock B 2,000 12% Stock C 3,000 15% Stock D 4,000 18% Portfolio 10,000 Return, Risk, and SML

Expected W Return*W 0.10 0.80% 0.20 2.40% 0.30 4.50% 0.40 7.20% sum 14.9% 7 Example 3) You have \$13,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 15% and Stock Y with an expected return of 9%. Assume your goal is to create a

portfolio with an expected return of 12.35%. How much money will you invest in Stock X and Stock Y? Return, Risk, and SML 8 Example 4) Portfolio Variance and Standard Deviation If we invest \$200 on stock A and invest \$800 on B, what is the portfolio variance? Return, Risk, and SML State of Econom y Probability of State of

Economy Boom Recessi on 50% 50% Stock Returns if State Occurs Stock A Stock B 0.70 -0.20 0.10 0.30

9 Solution #4) State of Probability Economy of State Boom 50% 0.70 0.10 0.220 0.210 0.010

0.00010 0.00005 Recession 50% -0.20 0.30 0.200 0.210 -0.010 0.00010

0.00005 0.20 0.80 Variance 0.0001 SD 0.01 Weight Return, Risk, and SML Stock Stock Portfilo

Squared Squared A B Portfolio Expected Deviation Deviation* Deviation Return Return Return Probability 10 Example #5) Portfolio Variance Consider the following information: State of Econo my

Probabil ity of State of Economy Boom Bust 0.67 0.33 Stock Returns if State Occurs Stock A Stock B Stock C 0.10 0.24

0.04 0.30 0.35 -0.15 What is the variance of a portfolio invested 22 percent each in A and B and 56 percent in C? Return, Risk, and SML 11 Components of Return Total return = Expected return + Unexpected return Expected return It is based on the markets understanding today of important factors that will influence the stock in the future Unexpected return

It is the risky part coming from unexpected information revealed in the future Return, Risk, and SML 12 Predicted Part GDP growth rate is one important factor that can affect almost every stock in the capital market Before the government announces GDP figures, the whole market will have a prediction of GDP growth The effect of this prediction on stock return is reflected in its expected return and current price Return, Risk, and SML 13 Possible Sources of Surprises Government figures released on gross domestic product (GDP) different from prediction A sudden, unexpected drop in interest rate News research projects Sales figure are higher than that expected

Unexpected release of new product by competitors Return, Risk, and SML 14 Components of Risks Total Risk = Systematic risk + Unsystematic risk Systematic risk (Market risk) Fluctuations that are due to market-wide news Systematic risk affects a large number of assets Unsystematic risk (Asset-specific risk) Fluctuations that are due to firm-specific news Unsystematic risk affects a limited number of assets Return, Risk, and SML 15

Examples of Two Types of Risks Systematic risk Oil price rise, increasing production costs The economy slows, reducing demand for the firms products Unsystematic risk The founder and CEO retires A product design is faulty and the product must be recalled Return, Risk, and SML 16 Portfolio Standard Deviation Return, Risk, and SML 17

Principles of Diversification Diversification: The process of spreading an investment across assets and thereby forming portfolios Principle of diversification Spreading an investment across many assets will eliminate some of the risk (diversifiable risk) There is a minimum level of risk (non-diversifiable risk) that cannot be eliminated simply by diversifying Return, Risk, and SML 18 Total Risks Number of Stocks Return, Risk, and SML 19

Diversifiable Risk Why some risk can be diversified away but some cannot? If we hold a large portfolio, some of stocks will go up in value because of positive firm-specific events and some will go down because of negative events The net effect on the overall value will be relatively small as these opposite effects will tend to cancel out each other Unsystematic risk can be eliminated by diversification, so diversifiable risk is essentially the unsystematic risk A relatively large portfolio has no unsystematic risk Return, Risk, and SML 20 Non-diversifiable Risk Marketwise news cause almost all the stock prices move in the same direction, so the net effect of market risk will be great Systematic risk cannot be eliminated by diversification, so non-diversifiable risk is essentially the systematic risk

A relatively large portfolio only has systematic risk Systematic risk principle The reward for bearing risk depends only on the systematic risk of an investment Return, Risk, and SML 21 Market Portfolio A portfolio of all stocks and securities traded in the capital markets Market portfolio has only systematic risk In practice, S&P 500 is used as the approximation for market portfolio Return, Risk, and SML 22 How to Measure Systematic Risk? Benchmark measure of systematic risk: Market portfolios standard deviation An assets Beta measures its systematic risk

Beta is a relative measure: How much systematic risk this asset has relatively to the market portfolio A market portfolio has a beta of 1 An asset with a beta of 0.5 has half as much as systematic risk as market portfolio An asset with a beta of 2 has twice as much as systematic risk as market portfolio Return, Risk, and SML 23 Beta for Selected Individual Stocks Return, Risk, and SML Company Consolidated Edison Hershey General Mills Industry

Utilities Food Processing Food Processing Beta 0.08 0.64 0.73 eBay Intel Apple Internet Service Semiconductors Computer Hardware 0.79 0.90 0.96

Google Salesforce.com Tiffany & Co. American Airline Internet Service Application Software Specialty Stores Major Airlines 1.07 1.30 2.15 3.85 24 Total Risk versus Beta Consider the following information: Standard Deviation Beta

Cisco 20% 1.43 Amgen 40% 0.58 Which stock has more systematic risk? Which stock has more total risk? Return, Risk, and SML 25 Portfolio Beta Weight of stock (Fraction of \$ invested in stock ) Beta of stock Portfolio Beta

Return, Risk, and SML 26 Example #6) Suppose we had following investments: Security Amount Invested Beta Stock A 1,000 0.80 Stock B

2,000 0.95 Stock C 3,000 1.10 Stock D 4,000 1.40 What is the beta of this portfolio? Does this portfolio have more or less systematic risk than the market portfolio? Return, Risk, and SML

27 Solution #6) Amount Security Invested Stock A 1,000 Stock B 2,000 Stock C 3,000 Stock D 4,000 Portfolio 10,000 Beta 0.80 0.95

1.10 1.40 W 0.10 0.20 0.30 0.40 sum Beta*W 0.0800 0.1900 0.3300 0.5600 1.16 This portfolio has more systematic risk than market portfolio, because its Beta is greater than 1. Return, Risk, and SML

28 Example #7) You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.29 and the total portfolio is equally as risky as the market. What must the beta be for the other stock in your portfolio? Return, Risk, and SML 29 Risk Premium Additional return investors earn by moving from a risk-free investment to a risky one Risk premium = Expected Return Risk-free rate Risk-free rate is the return from risk-free assets In practice, the return from Treasury bills is used as the approximation for risk-free

rate The reward for bearing systematic risk Return, Risk, and SML 30 Market Risk Premium Risk premium of market portfolio Difference between market portfolio expected return and risk-free rate Risk premium investors earn by bearing one unit systematic risk Reward for bearing one unit systematic risk Return, Risk, and SML 31 Risk Premium and Beta The return of large-company portfolio is essentially the return of S&P 500

index (proxy for market portfolio), so market premium can be view as the reward to bear one unit systematic risk If a stock has a beta of 2, how much risk premium should be awarded to investors who hold it? This stock has 2 units systematic risk Investor would expect 10% risk premium, why? Return, Risk, and SML 32 Capital Asset Pricing Model (CAPM) The CAPM defines the equilibrium relationship between risk premium, market risk premium, and beta

: expected return of risky asset : beta of risk asset : market portfolios expected return : risk-free interest rate Return, Risk, and SML 33 Example #8) A stock has a beta of 1.13, the expected return on the market is 10.7%, and the risk-free rate is 4.6%. What must the expected return on this stock be? Return, Risk, and SML 34 Reward to Risk Ratio Reward-to-Risk Ratio

= Risky asset is expected return = Return from riskless assets = Risky asset is beta In a well-organized, active market, the reward-to-risk ratio should be the same across all risky assets in equilibrium In a well-organized, active market, the reward-to-risk ratio should be the same as market risk premium in equilibrium Return, Risk, and SML 35 Example #9) Stock Y has a beta of 1.25 and an expected return of 12.6%. Stock Z has a beta of 0.8 and an expected return of 9.9%. a) If the market is now in equilibrium, what would the risk-free rate have to

be? b) If the risk free rate is 4.1% and market risk premium is 7%, are these stocks correctly priced? Why? Return, Risk, and SML 36 Security Market Line Return, Risk, and SML 37 Example #10) You are examining two stocks Bassett Inc and Hound Corporation. The risk free rate is 3% and the return of market portfolio is 8%. The following table provides some information. Next year Beta

a) Current Price Dividends (D1) Price (P1) Bassett 1.1 \$25 \$1.00 \$26.13 Hound 0.8

\$30 \$1.20 \$34.00 According to the CAPM, what is the expected return of the stock of Bassett Inc and Hound Corporation? b) What is the actual percent return of the stock of Bassett Inc and Hound Corporation? c) Draw the Security Market Line (SML), label axes, identify risk free asset and market portfolio. Identify where Bassett and Hound actually lie on this graph. d) If you buy 200 shares of Bassett and 200 shares of Hound and \$5,000 in Treasury bills, what would the portfolio beta be? Return, Risk, and SML 38

Example #11) You purchase 50 shares of Woods and 60 shares of Ogilvy. The risk free rate is 4% and the market premium is 5%. Data related to these two stocks is given below. Price Beta Standard Deviation of returns Woods \$25 0.9 45% Ogilvy \$35 1.1 25% a) According to the CAPM, what is the required return to your portfolio? b) At the end of one year, the price of Woods is now \$30 and the price of

Ogilvy is still \$35. You wanted to change the beta of this portfolio to 0.8, how many dollars would you have to spend on T-bills? Return, Risk, and SML 39

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