Case Study Assignment FNCE 561 You have been assigned to construct an optimal 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 (A&B); S&P 500 index; and 90-day Treasury Bills. Also shown are the annualized returns for each for the period specified. Portfolio A: Active Stock Selection Strategy Portfolio A is an actively managed US equity strategy that uses publicly available fundamental, 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, debt to equity ratio, 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. Portfolio A uses technical and sentiment factors to identify mispriced stocks by exploiting investor behavioral biases. Examples include momentum and price reversals where investors tend to over-react to good news by bidding up prices ABOVE fair value and over- react to bad news by bidding down prices BELOW fair value; short interest on a stock which indicates investor sentiment about a companys future prospects; share buybacks and dividend changes which can indicate a positive signal from managements optimism regarding a firms future prospects; and earnings surprise. Firms with favorable technical and sentiment factors also tend to outperform those stocks having less favorable factors. 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 having 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). Portfolio B: Global Macro Hedge Fund Portfolio B is a global macro hedge fund that 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 be 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 return 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, the portfolio will be long 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. As a macro hedge fund, Portfolio B is market neutral meaning that the long positions equal short positions thereby dramatically reducing systematic exposures. (e.g. low beta). Combining Portfolios, A & B Portfolios A & B are much more volatile than the risk-free rate. You will also find that their correlation is small indicating that there is a diversification benefit to be had from holding both in a portfolio (The correlation is now shown in the spreadsheet. 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 these two portfolios. In preparation for your upcoming meeting with the client, your boss asks that you perform the necessary calculations outlined below and be able to respond to the questions that follow. Hint: You will need to determine the correlations and volatilities for A & B. Analytical Assignment Complete the analytical portion of the case assignment in the excel template which can be found in Canvas. Formulas must reference parameters in other cells using absolute or relative cell references. DO NOT HARD CODE ANY NUMBERS IN YOUR EXCEL FORMULAS. 1) In the space provided in the Excel spreadsheet, plot the opportunity set for Portfolios A & B, the CAL & the indifference curve. To do this you will need to calculate the missing information in the table found in the Excel spreadsheet that accompanies the case using weights of portfolio A & B in 10 percentage point increments. This requires knowing how to program formulas in Excel using absolute and relative cell references from the data provided. (The table below already exists in the Excel file). 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 risky portfolio (e.g. the optimal allocation of A & B) using the concepts from Modern Portfolio Theory. The approximate optimal allocation can be determined using the table in Excel like the one shown above. You do not need to plot the CAL rather you can manually draw the CAL on the Excel graph (using Insert Shapes window in Excel) starting at the risk-free rate to the tangent point. 2) Find the optimal complete portfolio graphically using the clients indifference curve. 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. However, you will first need to calculate the utility of the optimal complete portfolio in the space provided in the Excel spreadsheet. The risk aversion coefficient (A) has been provided. Plot the indifference curve AND the opportunity set of risky assets on the same graph. Determine the optimal complete portfolio. You did this graphically above, but you need to calculate the precise composition of the optimal risky portfolio (recall ymaxU) and T-Bills (1-ymaxU). 3) In the space provided in the Excel spreadsheet, plot the CAPM regressions of 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-Bill. Calculate the following for each portfolio using the following methods in the spaces provided in the spreadsheet: a. Beta: using the Excel slope function b. Alpha: using the Excel y-intercept function. The return data is monthly, so the alpha via y-intercept function of the CAPM regression represents a MONTHLY alpha. c. Annualized alpha: using the CAPM formula and inputting annualized returns of each portfolio (A & B), S&P 500, risk free rate (T-Bills) and the beta calculated in part a above. Note that the annualized alphas of A & B are NOT the same as the monthly alphas multiplied by 12. The two may be close, but not exactly equal. d. Beta: using the beta formula. Recall the formula for beta which we derived and can be found in the Module 6 ppt lecture, Module 6 & 7 Notes, & the textbook. If you did parts a and d correctly, the two beta calculations will be EXACTLY the same. Upload the completed spreadsheet in Canvas Assignments under the Case Study_Analytical Solution. One submission per group. Intuition Questions After receiving a corrected analytical solution, should you then proceed with answering the intuition questions below to prepare for the meeting with the client. 1. Your client asks what the benefit is of combining the two portfolios to arrive at the optimal risky portfolio. Include in your explanation why the resulting portfolio that includes A & B has a higher Sharpe Ratio compared to Portfolio (A) or (B) by itself. Prepare a clear & concise response to your client. 2. Your client believes in the weak-form of market efficiency as it relates to security selection. Does Portfolio As performance provide sufficient justification to prove or disprove conclusively your clients belief that markets are weak-form efficient? Why or why not? 3. After further discussions with your client, it turns out that she believes markets are semi-strong form efficient as it relates ONLY to stock selection, what portfolio substitution(s) would you make to the recommended optimal risky portfolio and why? No calculations are necessary. 4. After meeting with the client, she informs you that she prefers a return higher than that of the optimal risky portfolio and is willing to accept the higher corresponding risk. a. Is it possible to achieve such a portfolio and if so, how would this be implemented? b. What does that indicate about your initial assumption(s) regarding the indifference curve? 5. Portfolio A returned 9.20% p.a. over the evaluation period compared to 5.00% p.a. for the S&P 500. This equates to a difference, or outperformance of 4.20% p.a. However, according to CAPM, the annualized alpha of portfolio A is 4.74% p.a. Explain the difference between the two numbers. (Note: It is not due to rounding) Upload the completed intuition questions in Canvas under Case Study Intuition Questions. One submission per group. Additional Information The case is designed to pull together investment principals covered throughout the course - specially Modules 4, 5, 6 & 7 and calculating geometric returns. It is based on a real-life project an investment management firm had done for a large pension client. Each step of the case builds upon the previous, so it is important students get each part of the analysis correct before moving on. If your 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 Please make a graph