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Consider a single-stock futures contract on Wal-Mart common stock. Assume that no dividends will be paid until after the expiration of the futures contract. Consider the following scenario:

Continuously compounded, annualized risk-free interest rate: r = 5%.

Current spot price of Wal-Mart stock: $65 per share.

Futures price on Wal-Mart single-stock futures: $65 per share.

Contract expiration: T = 0.25 year.

Does a risk-free arbitrage opportunity exist? If so, what is the basic strategy?

a.) No arbitrage opportunity exists at the moment.
b.) Yes. Buy Wal-Mart stock, invest at the risk-free rate, and enter a long position in Wal-Mart single-stock futures.
c.) Yes. Take a loan at the risk-free rate, buy Wal-Mart stock, and enter a short position in Wal-Mart single-stock futures.
d.) Yes. Sell Wal-Mart stock short, invest the proceeds at the risk-free rate, and enter a long position in Wal-Mart single-stock futures.
e.) Yes. Take a loan at the risk-free rate, sell Wal-Mart stock short, and enter a short position in Wal-Mart single-stock futures.

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Patrina Schowalter
Patrina SchowalterLv2
28 Sep 2019

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Consider a single-stock futures contract on Best Buy Co. The company will pay a quarterly dividend of $0.17 per share prior to expiration of the futures contract. Consider the following scenario. The stock goes ex-dividend in one month; for convenience, we will assume that the dividend is paid at that time. Assume that this dividend is the only one prior to expiration of the futures contract.

Annualized, continuously compounded risk-free interest rates: r1 = 3% for one month, and r2 = 4% for four months.

Current spot price of Best Buy stock: $23 per share.

Contract expiration: T = four months (1/3 of a year).

Futures price on Best Buy single-stock futures: $25 per share.

Does a risk-free arbitrage opportunity exist? If so, describe the general strategy.

a.) Borrow at the risk-free rates, buy shares of Best Buy, and enter a short position in Best Buy single-stock futures.

b.) Sell shares of Best Buy short, invest at the risk-free rates, and enter a long position in Best Buy single-stock futures.

c.) Sell shares of Best Buy short, invest at the risk-free rates, and enter a short position in Best Buy single-stock futures.

d.) Borrow at the risk-free rates, buy shares of Best Buy, and enter a long position in Best Buy single-stock futures

e.) No arbitrage opportunity exists.

Consider a single-stock futures contract on Exxon-Mobil stock. Consider the following scenario:

Annualized, continuously compounded risk-free interest rate for 3-month period: r = 3.79%.

Annualized, continuously compounded risk-free interest rate for 5-month period: r = 5.31%.

Current spot price of Exxon Mobil stock: $158 per share.

Dividend per share of $0.69 in 3 months.

Contract expiration: T = 5 months.

Futures price on Exxon Mobil single-stock futures: $150 per share.

An arbitrage opportunity exists. What is the net profit per share when the futures contract expires? Use a strategy that has zero net cash flows today.

Sabrina Gupta, an investment advisor with a major brokerage firm, was examining Wal-Mart Stores, Inc. (Wal-Mart) stock and its valuation. Gupta wondered whether to recommend the stock to any of her new clients or to existing clients who did not currently have Wal-Mart in their portfolios.

Her key task was to use an intrinsic value approach to price the shares and to then compare the resulting price with the price at which the stock was traded in the market. Gupta wanted to use alternative valuation methods and assumptions to produce intrinsic value estimates for Wal-Mart stock.

She was interested in seeing if the alternative methods would point to a consensus regarding the valuation of the stock and to see if the valuations suggested an investment opportunity given the current market price. Methods she contemplated to use were:

Multi-stage growth model

Price Earnings Multiple

Most valuation methods Gupta considered required a common set of inputs:

Future Cash Flows to Wal-Mart Investors

Growth rate of future cash flows

Discount factor or required rate of return by Wal-Mart investors

Gupta gathered data to determine each of the above.

Gupta thought that Dividends to Wal-Mart shareholders would adequately capture the cash flows to Wal-Mart shareholders; she also thought that this approach would simplify her task and she would revisit more complex valuation models if she felt the need.

Gupta thought that CAPM would provide her a relatively reliable estimate of the required rate of return. CAPM based required rate of return can be estimated by using a risk free rate, systematic risk of the firm and equity market risk premium. Gupta thought that in a valuation exercise that involve long term cash flows, 10-year government bond yield would be an appropriate risk free rate of return estimate. She checked the 10 year note rate and found out that it was about 3.68%. Gupta searched for Wal-Mart beta in Bloomberg. Bloomberg estimates betas by regressing the S&P 500 returns on the firm returns over the past two years and arrives at a “raw” beta estimate. Bloomberg makes an adjustment in raw beta based on some academic research. Gupta is confident that Bloomberg adjustment is justified and she uses Wal-Mart beta estimate of 0.66 in her analysis.

While Gupta is aware of the importance of EMRP assumption, she thinks that Bloomberg’s historical estimate of 5.05% is a safe assumption. She is aware of the fact that some studies suggest a larger risk premium of approximately six per cent, while others suggest a much lower forward-looking premium of less than four per cent. She is mindful of the arbitrariness of her assumption, and she takes a note to revisit this issue if her valuations produce unreasonable estimates.

Anticipated dividend growth (g) is often estimated in a variety of ways.

First, observed historical dividend growth can be assumed to continue in a perpetual fashion.

Second, future dividend growth can be estimated on the basis of recent estimates of analysts.

Gupta noted that the consensus annual Wal-Mart dividend for fiscal year 2011 was $1.21, and one respected analyst had estimated the expected constant dividend growth (in perpetuity) at approximately 3%.

As the chart suggests, both earnings and dividend growth rates are declining but they seem to be higher than the “respected analyst’s” estimates. Gupta decides to use several alternative perpetual growth assumptions to see the impact on price. Since Gupta decided to use variants of dividend discount model (DDM), she checked the anticipated earnings for 2011. Analyst’s estimates suggested $4.10 earnings per share. Gupta decided to use 10% growth rate from 2011 to 2012 and assumed a steady decline to 3% in 13 years (until 2024) where the perpetual growth rate of 3% resumes. She also assumed that WalMart will increase its dividend payout ratio from 30% to 55% from years 2012 to 2024. You are asked to reproduce Gupta’s analysis of multi-stage growth model and double check her valuation by using an earnings multiple. You have all the data you need to conduct the multi stage discounted growth model analysis, but you will need to do some research about the multiples valuation.

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