AcF 214 Tutorial Week 5

Question 1. a) Average return:

b) Covariance between the stocks?

c) Correlation between these two stocks?

Question 2.

Question 3. Calculate the expected return and the volatility of a portfolio that is equally invested in the stocks. a) b)

Question 4. The CAPM Assumptions:  1. Investors can buy and sell all securities art competitive market prices (without incurring taxes or transactions costs) and can borrow and lend at the risk-free rate.  2. Investors hold only efficient portfolios of traded securities – portfolios that yield the maximum expected return for a given level of volatility.  3. Investors have homogenous expectations regarding the volatilities, correlations, and expected returns of securities.

a) Find the portfolio with the same expected return as Microsoft but with the lowest possible volatility: Under the CAPM assumptions, the combination of the risk-free investment and the market portfolio has the highest expected return for a given volatility and the lowest volatility for a given expected return. By holding a leveraged position in the market portfolio you can achieve an expected return of: Setting this equal to 12% gives Question 4. Your investment portfolio consists of $15,000 invested in only one stock—Microsoft. Risk-free rate is 5%, Microsoft stock has an expected return of 12% and a volatility of 40%, market portfolio has an expected return of 10% and a volatility of 18%.

Note that this is considerably lower than Microsoft’s volatility. So the portfolio with the lowest volatility that has the same return as Microsoft has in the market portfolio and borrows that is -$6,000 in the in riskless asset. Volatility of this portfolio:

b) Find the portfolio with the same volatility as Microsoft but with the highest possible expected return: Setting this equal to the volatility of Microsoft gives So the portfolio with the highest expected return that has the same volatility as Microsoft has in the market portfolio and borrows, that is, it has -$18, in the in riskless asset. Note that this is considerably higher than Microsoft’s expected return. Expected return of this portfolio:

Question 5. r f = 4%, Market: R Mkt = 10%, SD(R Mkt )=16% J&J: SD(R JJ )=20%, Corr(R JJ, R Mkt )=0.06 a) Johnson and Johnson’s beta ?

b) Under CAPM, its expected return?

Question 6.

Question 7. Risk premium of zero-beta stock? What happens if we substitute a zero-beta stock in a portfolio with a risk-free asset?  The risk premium of a zero-beta stock is zero  If you substitute a zero beta stock with a risk free asset, the expected return of the portfolio will remain the same but the volatility will go up  One can show (by using the familiar formula for the variance of the portfolio) that replacing zero-beta stock by the risk-free asset in the market portfolio will result in a new portfolio with a higher volatility (see next slide)

The variance of portfolio P consisting of a zero-beta asset, that is, an asset uncorrelated with this portfolio, and the remaining set of assets called collectively A can be written as: where w and (1-w) denote the fractions of wealth invested in the zero-beta assets and assets A, respectively. To find the unknown cov(A, zβ), we use the fact that the zero-beta asset is uncorrelated with the reference portfolio:

Consequently, The latter being the variance of the original portfolio P with the zero- beta asset replaced with the riskless asset.