Question

You have been assigned to construct an optimal 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 S&P 500 index; and 90-day Treasury Bills. Also shown are the annualized returns for each for the period specified. 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 mispriced stocks 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 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 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 exposure (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 (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 AssignmentThe 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 calculate the missing information in the table from the Excel spreadsheet that accompanies the case using weights of portfolio A & B in 10 percentage point increments. To do this you will need to know 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 AWeight Port BReturn Standard DeviationSharpe Ratio0%100%1090208030704060505060407030802090101000Determine the optimal risky portfolio (e.g. the optimal allocation of A & B) using the concepts from Modern Portfolio Theory draw in the Capital Allocation Line (CAL). The approximate optimal allocation can be determined using the table in Excel like the one shown above. Or you can obtain a more precise optimal allocation using the formula shown in Chapter 7 (equation 7.13). Students are also encouraged to use 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 utility theory concepts to determine a more precise allocation of the optimal risky portfolio (ymaxU) and T-Bills (1-ymaxU). 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) is explained in the Modules 6 & 7 Notes; ppt lecture notes; and text book. Recall the covariance between two assets (A & B) is the volatility of asset A times the volatility of asset B times the correlation between A & B. Then calculate the alpha for each portfolio A & B using the intercept function in Excel and the CAPM formula solving for alpha. Note the two CAPM regressions 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, 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 ONLY 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. i. Is this possible to achieve and if so, how? ii. 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)Additional RequirementsOrganize and present your results neatly and be prepared to discuss.

Answer 1

SOLUTION:-

Given that

Weak form efficiency claims that past price movements, volume and earnings data do not affect a stock’s price and can’t be used to predict its future direction.Weak form efficiency, also known as the random walk theory, states that future securities' prices are random and not influenced by past events. Advocates of weak form efficiency believe all current information is reflected in stock prices and past information has no relationship with current market prices.Unlike weak form efficiency, the other forms believe that past, present and future information affects stock price movements to varying degrees.The key principle of weak form efficiency is that the randomness of stock prices make it impossible to find price patterns and take advantage of price movements. Specifically, daily stock price fluctuations are entirely independent of each other; it assumes that price momentum does not exist. Additionally, past earnings growth does not predict current or future earnings growth.Weak form efficiency doesn’t consider technical analysis to be accurate and asserts that even fundamental analysis, at times, can be flawed. It’s therefore extremely difficult, according to weak form efficiency, to outperform the market, especially in the short term. For example, if a person agrees with this type of efficiency, they believe that there’s no point in having a financial advisor or active portfolio manager. Instead, investors who advocate weak form efficiency assume they can randomly pick an investment or a portfolio that will provide similar returns.

So given the portfolio A was constructed,its basis doesn't advocate weak form efficiency.

No portfolio A's performance is not a justification to weak form of market efficiency.