You have been assigned to construct the optimal portfolio comprising two risky assets (Portfolios A & B) while considering the client’s risk tolerance. The attached spread sheet shows historical monthly returns of the two portfolios, the S&P 500 and 90day Treasury Bills. Also shown are the annualized returns for each for the period specified.
1.The first risky asset (Portfolio A) is a US equity strategy that uses publically available valuation, technical and sentiment factors to assess which stocks are overpriced and which are underpriced. Fundamental factors indicate the magnitude and quality of a company’s earnings and the strength of its balance sheet. Examples of such factors include: cash flow growth, cash flow return on invested capital, price to cash flow, and accruals which assess earnings quality (low quality earnings indicate that management may be manipulating earnings by adjusting accruals). Companies with favorable fundamental factors tend to outperform those with less favorable factors.
2.Technical and sentiment factors seek to identify mispricings resulting from investor behavior. Examples include: momentum and price reversals where investors tend to overreact to good news by bidding up prices ABOVE fair value and bad news by bidding down prices BELOW fair value; short interest on a stock which can indicate the investor sentiment about the company’s prospects; share buybacks which can indicate a positive signal from management’s optimism regarding a firm’s future prospects; and earnings / revenue surprise. Firms with favorable technical and sentiment factors also tend to outperform. For example, firms whose earnings and revenue exceed analysts’ expectations tend to continue to outperform vs. those firms that experience earnings surprise due to cost cutting.
3.Starting with the market portfolio, the US equity strategy overweights those stocks with more favorable fundamental, technical and sentiment factors and underweights or avoids those stocks with lessfavorable or unfavorable factors. The strategy seeks to outperform the market portfolio as represented by the S&P 500. The monthly returns of the
US
4.The second risky asset (Portfolio B) is a global macro hedge fund. This strategy seeks to benefit from mispricings within and across broad asset classes by taking long and short positions in equity markets, bond markets and currencies. For example, if the manager believes that US equities will outperform Japanese equities, the portfolio will go long S&P 500 futures and short TOPIX futures (TOPIX is a Japanese equity index). This long/short trade is not impacted by the overall direction of global equities, but rather the relative movement between US and Japanese equities. Similarly for bonds, if the manager believes that interest rates in the United Kingdom (UK) will decline more so than interest rates in Australia, then the manager will buy UK gilt futures (gilt is the 10year UK bond) and short Australian 10year bond futures. Again, this trade is not impacted by the overall direction of global interest rates, but rather the relative movement between
UK
5.Portfolios A & B are much more volatile than the risk free rate. You will find that their correlation is small indicating that there is a diversification benefit to be had from holding both in a portfolio (I don’t show the correlation, but you will need to calculate this using the excel function “=correl(range 1, range2)”.
You will be meeting with a client that is looking for investment advice from you based on your two strategies A & B. In preparation for your upcoming meeting with the client, your boss asks that you respond to the questions below and be ready to discuss. Hint: You will need to determine the correlations and volatilities for each risk premium.
Analytical Assignment
Weight Port A 
Weight Port B 
Return 
Standard Deviation 
Sharpe Ratio 
0% 
100% 

10 
90 

20 
80 

30 
70 

40 
60 

50 
50 

60 
40 

70 
30 

80 
20 

90 
10 

100 
0 
Determine the optimal allocation of A & B and draw in the Capital Allocation Line (CAL). You can arrive at an approximate optimal allocation using a table similar to the one shown above OR you can obtain a more precise optimal allocation using the formula shown in Chapter 7 (equation 7.13). When drawing the
CAL
Expected Return 
Standard Deviation 
5% 

7.5 

10 

12.5 

15 

17.5 

20 

22.5 

25 
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 yintercepts using the two different methods.