MT480 Unit 5 Risk and Return Analysis Example

What Diversification Strips Away: An MT480 Unit 5 Analysis of Risk and Return in a Mushroom Grower's Stock

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Purdue University Global

MT480: Corporate Finance

Unit 5 Risk and Return Analysis

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[Date]

Brandywine Hollow Mushrooms, the gas producer, the scenarios and every figure are composite; the sources cited are real.

Why Gas Prices

Brandywine Hollow Mushrooms burns natural gas to pasteurize compost and to heat its growing rooms in winter. Gas is its largest cost after labor, so its profits fall when gas prices spike and rise when gas is cheap. A natural gas producer has the opposite exposure. Pairing the two shows what diversification does.

The Scenarios

Four states of the coming year are assigned probabilities. A gas spike in a strong economy, probability 20 percent: the grower returns negative 0.6 percent, held up by strong demand; the producer returns 26.1 percent. A gas spike in a weak economy, 15 percent: the grower returns negative 15.3 percent; the producer 19.0. A normal year, 40 percent: the grower 15.2 percent; the producer 8.7. A gas glut, 25 percent: the grower 22.9 percent; the producer negative 13.6.

Expected Return and Risk for Each Stock

Each stock's expected return weights its four scenario returns by their probabilities. For the grower, it is about 9.39 percent; for the producer, about 8.15 percent. Standard deviation captures how far the scenario returns stray from that average, with each squared gap weighted by its probability. The grower's is about 13.06 percent; the producer's about 14.16. Each stock alone is risky: in a bad year the grower could lose 15 percent, and the producer 14.

The Two Together

The two stocks move against each other. Their correlation across the scenarios is about negative 0.80: when gas spikes, the grower falls and the producer rises. A portfolio holding 60 percent grower and 40 percent producer has an expected return equal to the weighted average, about 8.89 percent. Its standard deviation is far lower than either stock's, about 4.72 percent, because the losses in one stock are largely offset by gains in the other. In the four scenarios the portfolio returns 10.08, negative 1.58, 12.6 and 8.3 percent.

Holding both stocks gives up half a point of expected return and removes almost two-thirds of the risk.

Markowitz (1952) showed that combining assets changes risk through their co-movement as much as through each asset's own volatility, and this pair is an unusually clear example. Few real stocks are as negatively correlated as these two; most diversification comes from combining many stocks whose returns are only loosely related.

What the Market Pays For

If diversification removes much of a stock's risk, investors cannot expect to be paid for bearing that part. The capital asset pricing model, developed by Sharpe (1964), holds that the market rewards only systematic risk, the share of a stock's swings tied to the broad market, which no amount of diversification removes. That risk is measured by beta.

With Treasury bills at 4.3 percent, a 5.5-point premium for the market and a beta of 0.84 estimated from sixty months of returns, the grower's required return is 4.3 percent plus 0.84 times 5.5 percent, about 8.92 percent. The scenario analysis expects 9.39 percent, about 0.47 points above the security market line, which would suggest the stock is slightly underpriced if the scenarios are right.

How Much of the Risk Is Systematic

Beta explains about 23.9 percent of the variance in the grower's monthly returns over the sixty months. The other 76 percent comes from events specific to the grower and its industry, gas prices, crop losses, grocery contracts, which a diversified investor can largely offset. That is why the grower's total standard deviation, 13.06 percent, overstates the risk a diversified shareholder actually bears, and why its required return is lower than its volatility might suggest.

What the Grower's Managers Should Take From This

The analysis matters inside the company as well as to investors. Managers often want to reduce the volatility of earnings by hedging gas prices or by diversifying into businesses that move differently. The capital asset pricing model suggests caution: shareholders who already hold diversified portfolios do not need the company to diversify for them, and they will not pay more for a stock simply because its earnings are smoother. Hedging can still be worth doing when volatility itself is costly, for example when a gas spike could breach a loan covenant or force the company to cut a promised delivery, as nearly happened in Unit 1. The justification has to be that cost, not the volatility alone. Unit 9 returns to the covenant question when it weighs how much debt the grower can carry through a gas-spike year.

Limits

The scenario probabilities and returns are judgments, and different analysts would assign different ones. Beta is estimated from past returns and may not hold in the future. Fama and French (2004) review evidence that the capital asset pricing model explains average returns imperfectly, so the 8.92 percent figure is a reasonable estimate rather than a precise one. Unit 7 uses it in the cost of capital and tests how much the answer changes if beta is higher or lower.

References

Fama, E. F., & French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25-46. https://doi.org/10.1257/0895330042162430

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425-442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x