Use the capital asset pricing model (CAPM) to determine the beta and alpha of Portfolio A & Portfolio B. Show the CAPM relationship graphically for BOTH Portfolio A and Portfolio B (separate graphs). The market portfolio is represented by the S&P 500 and the risk free rate is represented by 90 day Treasury Bill. Determine the beta for portfolio A & B using: i) the slope function in Excel; and ii) the formula for beta – the co-variance between the asset and the market divided by the variance of the market. This is explained in the Modules 6& 7 notes and pages 296 & 297 in the text. Recall the covariance between two assets is the volatility of asset 1 times the volatility of asset 2 times the correlation between them.
Calculate the expected alpha for each portfolio A & B using the intercept function in Excel and the index model of CAPM formula (equation 9.9 on page 302 – note that the terms are in excess return form). Ignore the error term and you have all the information to solve for alpha based on the monthly returns. Compare the betas and y-intercepts using the two different methods.
The client will notice that the Sharpe ratio of the hedge fund (Portfolio B) is much higher than that of the equity strategy (Portfolio A) and will ask why the optimal risky portfolio wouldn’t be 100% of Portfolio B. How would you respond?
Your client vehemently believes in the semi-strong form of market efficiency as it relates to security selection. Is the performance of Portfolio A sufficient justification to convince the client otherwise – that markets are inefficient or at least less efficient? Why or why not?
Given your client’s belief regarding market efficiency as it pertains to security selection, what portfolio substitution(s) would you make in your optimal portfolio? No calculations are necessary to answer this.
Your client is expected to ask why you are recommending the optimal complete portfolio instead of the optimal portfolio even though the latter has a higher expected return. How will you respond?
After meeting with the client, she appears to prefer the risk/return trade-off of the optimal portfolio rather than that of the optimal complete portfolio. What does that indicate about your initial assumptions regarding the indifference curve?
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