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Equity Homework Review Packet CHAPTERS 1 - 4 (ELEMENTS OF INVESTMENTS) 1. On October 8th 2008, Warren Buffet purchased $5B of Goldman Sachs preferred stock with par value of $0.01 per share alongside a warrant (a long-dated option) to purchase 43,478,260 shares at a strike price of $115 and an expiration date of October 2013. The underlying stock was trading at $111 per share and the stock fell to $52 just over one month later. The preferred stock paid Buffet a coupon rate of 10%. At that time, Goldman Sachs demonstrated tangible book value of $37.266B with 394.53MM shares outstanding. Total company debt approximated $462.5B. a. Did Buffet’s investment increase, decrease, or not change the risk of bankruptcy for Goldman Sachs? Why? (2 points) b. If Goldman had gone bankrupt, rank the order of liquidation preference for company debt, preferred stock, and common equity on a scale of 1 to 3 with 1 indicating greatest preference. Assume that all company debt ranked pari passu. (3 points) c. Although not stated above, would you guess that the preferred stock received or did not receive voting rights? Why or why not? (2 points) d. At what percentage of pro forma tangible book value, adjusted for Buffet’s investment, did Goldman’s equity trade at that time? (2 points) e. If Goldman’s equity had traded to 200% of adjusted tangible book value, what would Buffet’s warrants have been worth? (2 points) CHAPTERS 5 – 9 (PORTFOLIO THEORY) 2. Abigail Grace is twenty-seven years old with a net worth of $5MM. She rents a luxury apartment in downtown Philadelphia. She owns an actively managed equity mutual fund with a portfolio of 500 stocks where Abigail’s shares are worth $4MM. She owns a bond index fund where her shares are worth $1MM. a. Abigail’s actively managed equity mutual fund has been a top quartile performer for two consecutive years. How likely is it that this fund is a top quartile performer during 2021 and a top decile performer during 2022? (2 points)? Why (2 points)? b. Abigail’s brother Lance manages a long/short equity hedge fund that owns just 20 stocks and shorts 15-20 stocks. Lance tells Abigail, “Using CAPM, I have forecast alpha for each of the 500 stocks in the S&P 500, and I buy the stocks offering the most alpha while I short the stocks offering the least alpha.” How likely is Lance’s fund to generate alpha going forward (1 point)? Why (1 point)? c. Abigail’s brother-in-law Mason is the Chief Investment Officer for a major pension fund. He tells Abigail, “I analyzed Lance’s performance using French & Fama’s 3-Factor Model, and his fund generates no real alpha.” What might explain this discrepancy (2 points)? d. Abigail asks Mason for a stock idea, and Mason offers to her, “Our top equity manager is heavily invested in Apple. Using French & Fama’s 3-Factor Model, he projects alpha of 10%, Market Beta of 180%, SMB (size factor) Beta of -10%, and HML (value factor) Beta of 80% for the next 12 months. Construct an arbitrage strategy for Abigail using this information (3 points). Use specific dollar weights for any securities you recommend. e. The projected return for the Market is 5%, the projected return for a SMB factor index is 11%, the projected return for an HML factor index is 7%, and the risk-free rate is 2%. How much profit will the arbitrage strategy in (d) above generate (2 points)? 3. After Abigail realizes the profit from her arbitrage strategy using Microsoft stock, she spends the proceeds on a trip to Monaco. She then asks Mason to review her portfolio. He suggests replacing her shares in the actively managed mutual fund for shares in an ETF that tracks the Wilshire 5000. Mason also suggests rebalancing the weights of equity and bonds in her portfolio. Over the last 15 years, the equity index ETF has generated geometric average annual returns of 9% with a standard deviation of 11%. Abigail’s bond index has returned 3% with a standard deviation of 4% over the same time period. Mason’s analysts are projecting the following returns for these index funds across four economic conditions during the next twelve months: a. If the optimal combined portfolio consists of 70% bonds and 30% equities, what is the forecast return for the combined portfolio during the next twelve months (3 points)? b. Using the forecast returns across the four economic scenarios, what is the forecast standard deviation for the combined portfolio during the next twelve months? (10 points) c. If the forecast returns above are normally distributed, use Value at Risk to determine your minimum annual return 67% of the time (2 points). 4. Abigail ponders the figures in #3 above, and she decides that she wants more return going forward despite the additional risk involved. a. If Abigail can borrow 50% of the value of her unleveraged $5MM combined portfolio at the risk-free rate of 2.0%, what is the maximum annual return she can achieve using the efficient combined portfolio from #4 above (3 points). b. Using the leveraged portfolio in (a) above and using Value at Risk, determine Abigail’s smallest expected loss (in dollars) among the worst 2.5% of expected outcomes during the next twelve months (2 points). c. If the maintenance margin is 40%, how much could Abigail’s combined leveraged portfolio decline (in % or $) before she receives a margin call (2 points)? 5. Growth and value can be defined in several ways. Growth usually conveys the idea of a portfolio emphasizing or including only companies believed to possess above-average future rates of per-share earnings growth. Low current yield, high price-to-book ratios, and high price-to-earnings ratios are typical characteristics of such portfolios. Value usually conveys the idea of portfolios emphasizing or including only issues currently showing low price-to-book ratios, low price-to-earnings ratios, above-average levels of dividend yield, and market prices believed to be below the issues’ intrinsic values. a. Identify and provide reasons why, over an extended period, value-stock investing might outperform growth-stock investing. (2 points) b. Explain why the outcome suggested in (a) should not be possible in a market widely regarded as being highly efficient. (2 points) c. What is your current personal belief regarding the level of domestic market efficiency? Cite evidence from class to support your belief (2 points). How would you incorporate evidence around the growth versus value debate into your own investment approach (2 points)?