Case Study Assignment

You have been assigned to construct a portfolio comprising two risky assets (Portfolios

A & B) while considering your clients 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

companys 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 companys prospects; share buybacks which can indicate a

positive signal from managements optimism regarding a firms 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. To do this 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 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). 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 Excels

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 clients 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 As 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: Its not due to rounding)

Additional Requirements

Organize and present your results neatly and be prepared to discuss.

The case is designed to pull together investment principals you learned throughout the

course and is based on an exercise I had done for a pension client.

Each step of the case builds upon the prior so its important that you get each part

correct before moving on. If youre group is struggling, please let me know ASAP and we

can discuss via email or phone. Please do not wait until the last minute to start working

on the case.