You have been assigned to construct a portfolio comprising two risky assets (Portfolios A B) while considering your client's risk tolerance.

You have been assigned to construct a portfolio comprising two risky assets (Portfolios A & B) while considering your client's risk tolerance. The attached spread sheet shows historical monthly returns of the two portfolios; the market portfolio as represented by the S&P 500 index; and the risk free rate as represented by 90-day Treasury Bills. Also shown are the annualized returns for each investment during the period. 

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 over-priced and which are under-priced. 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. 

Technical and sentiment factors seek to identify mis-pricings resulting from investor behavior. Examples include: momentum and price reversals where investors tend to over-react 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.

Starting with the market portfolio, the US equity strategy over-weights those stocks with more favorable fundamental, technical and sentiment factors and under-weights or avoids those stocks with less-favorable or un-favorable factors. The strategy seeks to out-perform the market portfolio as represented by the S&P 500. The monthly returns of the US equity strategy are shown in the attached spreadsheet (Portfolio A).

The second risky asset (Portfolio B) is a global macro hedge fund. This strategy seeks to benefit from mis-pricings 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 out-perform Japanese equities, the portfolio will go long S&P 500 futures and short TOPIX futures (TOPIX is an index that serves as a proxy for Japanese equities). 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 10-year UK bond) and short Australian 10-year bond futures. Again, this trade is not impacted by the overall direction of global interest rates, but rather the relative movement between UK and Australian rates. Recall that bond prices rise as interest rates decline. The global macro hedge fund is mostly market neutral meaning that long positions equal short positions thereby dramatically reducing systematic exposures (low beta). 

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 (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 the 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

The analytical portion of the case assignment should be completed in the excel template which can be found in Canvas.

1.Plot in Excel the risky asset opportunity set for Portfolios A & B. You will need to create the following table in Excel assuming weights of portfolio A & B in 10 percentage point increments. Then calculate expected return; standard deviation; and Sharpe ratio for each allocation to A & B. Your table in the Excel file should look like the one below.

Weight Port AWeight Port BReturn Standard DeviationSharpe Ratio

0%100%

1090

2080

3070

4060

5050

6040

7030

8020

9010

1000

Determine the optimal allocation of A & B and draw in the Capital Allocation Line (CAL). The approximate optimal allocation can be determined using a table like the one shown above. Or you can obtain a more precise optimal allocation using the formula shown in Chapter 7 (equation 7.13). Some students have used Excel's Solver function to find the optimal risky portfolio - that is also acceptable. When drawing the CAL on the efficient frontier graph plotted in Excel, you can manually draw a line starting at the risk free rate to the tangent point.

2.Find the optimal complete portfolio based on your client's indifference curve. Hint: Plot an indifference curve on the same graph you just created using the utility function formula from Chapter 6. To make things easier, you can use the same portfolio risk numbers from the table above and then calculate the expected return based on U = 9% and a risk aversion coefficient A = 10. Plot the indifference curve AND the opportunity set of risky assets on the same graph.  

Next determine the optimal complete portfolio. While this can be done graphically, you need to use the formula to determine a more precise allocation between the optimal risky portfolio and T-Bills. 

3.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 T-Bills. Determine the beta for portfolio A & B using the following methods:

i.The slope function in Excel, and 

ii.The beta formula (co-variance divided by the market variance) 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 A times the volatility of asset B times the correlation between them. 

Then calculate the 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. Note the two regressions you did are based on monthly returns so the y-intercept (or alpha) is a MONTHLY alpha. 

If you plug the annualized returns of the respective portfolio (A or B); the S&P 500; and T-Bills into equation 9.9, the alpha you calculate will be an ANNUALIZED alpha. 

Intuition Questions 

a.Your client asks why you would combine the lower returning portfolio (A) with portfolio (B) in arriving at the optimal risky portfolio. What is your response? 

b.Your client believes in the weak form of market efficiency as it relates to security selection. Is Portfolio A's performance sufficient justification to prove this belief? Why or why not?

c.Assume your client believes in the strong-form of market efficiency as it relates to security selection, what portfolio substitution(s) would you make to your optimal risky portfolio? No calculations are necessary.

d.After meeting with the client, she informs you that she prefers a return higher than that of the optimal risky portfolio. Is this possible to achieve and if so, how? What does that indicate about your initial assumptions regarding the indifference curve?

e.Portfolio A returned 5.86% p.a. over the evaluation period compared to a 2.57% p.a. for the S&P 500. This equates to a difference or outperformance of 3.29% p.a. According to the CAPM, the annualized alpha of portfolio A is 3.32% p.a. Explain the difference between the two numbers. (Note: It's not due to rounding)

DATA for Questions:

Portfolio APortfolio BS&P 50090dBillRm - RfRA - RfRB - Rf

Mar 01-4.50%-1.10%-6.34%0.44%-6.78%-4.94%-1.54%

Apr 018.75%1.38%7.77%0.38%7.39%8.37%1.00%

May 011.03%-7.13%0.67%0.37%0.30%0.66%-7.50%

Jun 01-2.45%3.68%-2.43%0.32%-2.76%-2.77%3.36%

Jul 01-1.87%2.72%-0.98%0.31%-1.30%-2.18%2.40%

Aug 01-3.77%13.44%-6.26%0.30%-6.56%-4.07%13.14%

Sep 01-7.43%-2.11%-8.08%0.29%-8.36%-7.72%-2.39%

Oct 012.09%2.51%1.91%0.26%1.65%1.83%2.25%

Nov 015.94%4.24%7.67%0.21%7.46%5.73%4.02%

Dec 011.99%10.09%0.88%0.18%0.70%1.81%9.91%

Jan 02-1.18%1.27%-1.46%0.16%-1.62%-1.33%1.11%

Feb 02-1.45%-0.56%-1.93%0.13%-2.06%-1.58%-0.69%

Mar 024.95%-0.86%3.76%0.15%3.61%4.81%-1.01%

Apr 02-5.28%3.56%-6.06%0.14%-6.21%-5.43%3.41%

May 02-0.68%-1.62%-0.74%0.15%-0.89%-0.83%-1.77%

Jun 02-8.26%7.47%-7.12%0.14%-7.27%-8.41%7.32%

Jul 02-7.03%-2.09%-7.79%0.15%-7.94%-7.18%-2.24%

Aug 020.80%3.40%0.66%0.14%0.51%0.66%3.26%

Sep 02-10.07%-0.32%-10.87%0.14%-11.01%-10.21%-0.46%

Oct 026.93%2.82%8.80%0.14%8.66%6.79%2.68%

Nov 024.13%4.95%5.89%0.13%5.76%4.00%4.82%

Dec 02-4.99%-5.70%-5.87%0.12%-5.99%-5.11%-5.82%

Jan 03-2.11%5.90%-2.62%0.11%-2.73%-2.22%5.79%

Feb 03-1.51%-6.23%-1.50%0.09%-1.59%-1.60%-6.32%

Mar 031.66%1.78%0.97%0.10%0.87%1.56%1.68%

Apr 036.85%3.24%8.24%0.10%8.14%6.76%3.15%

May 035.13%10.52%5.27%0.10%5.17%5.04%10.43%

Jun 031.11%1.09%1.28%0.09%1.18%1.02%1.00%

Jul 031.96%-17.02%1.76%0.09%1.68%1.87%-17.10%

Aug 032.37%1.77%1.95%0.08%1.87%2.29%1.69%

Sep 03-0.23%13.19%-1.06%0.08%-1.14%-0.30%13.11%

Oct 035.56%12.80%5.66%0.08%5.58%5.48%12.72%

Nov 031.48%3.82%0.88%0.08%0.80%1.40%3.74%

Dec 034.23%4.50%5.24%0.08%5.16%4.15%4.43%

Jan 042.24%8.29%1.84%0.08%1.76%2.16%8.21%

Feb 042.34%7.74%1.39%0.07%1.32%2.27%7.67%

Mar 04-0.86%4.09%-1.51%0.08%-1.59%-0.94%4.01%

Apr 04-2.23%-9.22%-1.57%0.08%-1.65%-2.30%-9.30%

May 041.88%1.35%1.37%0.08%1.29%1.80%1.27%

Jun 042.50%-1.96%1.94%0.08%1.86%2.42%-2.04%

Jul 04-3.94%8.12%-3.31%0.10%-3.40%-4.03%8.02%

Aug 04-0.19%-2.86%0.40%0.11%0.30%-0.30%-2.97%

Sep 041.42%1.15%1.08%0.12%0.96%1.30%1.04%

Oct 041.96%0.62%1.53%0.13%1.39%1.82%0.48%

Nov 045.21%6.39%4.05%0.14%3.90%5.06%6.25%

Dec 043.23%0.44%3.40%0.16%3.24%3.07%0.28%

Jan 05-2.72%1.18%-2.44%0.18%-2.62%-2.90%1.00%Beta =0.924

Feb 052.57%9.27%2.10%0.18%1.93%2.40%9.10%y-int =0.26%

Mar 05-0.58%-1.09%-1.77%0.21%-1.98%-0.79%-1.30%

Apr 05-2.07%-3.82%-1.90%0.22%-2.11%-2.29%-4.04%

May 053.84%-0.06%3.18%0.24%2.94%3.60%-0.29%

Jun 050.66%5.31%0.14%0.24%-0.09%0.42%5.07%

Jul 054.16%2.78%3.72%0.25%3.47%3.90%2.52%

Aug 05-0.72%-1.15%-0.91%0.27%-1.18%-0.99%-1.42%

Sep 051.96%7.09%0.81%0.27%0.54%1.69%6.82%

Oct 05-2.02%2.84%-1.67%0.29%-1.96%-2.31%2.55%

Nov 054.75%5.94%3.78%0.30%3.48%4.45%5.64%

Dec 050.83%-4.20%0.03%0.32%-0.28%0.51%-4.52%

Jan-064.15%1.17%2.65%0.33%2.31%3.82%0.84%

Feb-060.05%2.23%0.27%0.32%-0.05%-0.27%1.92%

Mar-061.00%-5.05%1.24%0.37%0.87%0.63%-5.42%

Annualized Return5.86%24.64%2.57%2.19%

Annualized Volatility13.4%19.0%14.2%0.3%14.2%13.4%19.0%

A =10Beta =0.211

U =9.0%y-int =1.79%

Weight AWeight BExp RtnExp RiskSharpeIndifference curve Exp Rtn

0.01.024.64%

0.10.922.76%

0.20.820.88%

0.30.720.88%

0.40.620.88%

0.50.515.25%

0.60.415.63%

0.70.315.07%

0.80.214.52%

0.90.113.96%

1.00.013.40%