# Risk Measures and Capital Allocation

Capital allocation is critical to a firm’s market risk management. It involves setting limits on all activities and giving priority, in resource allocation, to areas expecting the greatest reward. When wisely allocating capital, a company ensures that all its risk appetite is not used up by strategies whose productivity is unproven. This ensures that areas that are most likely to succeed are not deprived of the capital they require.

Capital is relatively expensive and should, therefore, be injected into activities with the best chance of earning a relatively higher return. Alternatively, capital can be funneled into areas with the most significant expertise and strategies that investors believe can be executed successfully.

Economic capital is the amount of shareholders’ equity needed by a company for survival in a worst-case scenario. Economic capital measurement is the first step in capital allocation. A minimum amount of economic capital is established to ensure that a company’s risk does not exceed its available capital. Therefore, the measurement of a company’s risk appetite is pegged on its economic capital. The risk appetite is similarly subdivided among a firm’s units and this informs risk budget-related decisions.

Capital allocation is useful in cases where a portfolio uses all the leverage or where the strategy has a tail risk that is greater than expected. Economic capital measures the amount of shareholders’ equity that may be required to meet the tail risk losses. Capital allocation, on the other hand, measures the proportion of capital put at risk by a strategy that focuses on losses at a very high confidence level.

An investor may put a hurdle rate over a specified period to ensure optimal use of capital. The hurdle rate can assume the form of the expected rate of return relative to a unit of capital allocated. Let us use an example to illustrate this. Assume that portfolios A and portfolio B require $100,000 and$250,000, respectively. Further, assume that the expected return for A is $18,000 (18%) per year, while that of portfolio B is$30,000 (12%) per year. If an investor’s annualized hurdle rate is 15%, then portfolio A appears to have better use of capital relative to portfolio B, which has a relatively higher income.

## Question

An investor X has three portfolio choices to invest in. The portfolios A, B, and C require capitals of $500,000,$400,000, and $1,000,000, in that order. If the expected return for A is$95,000, B is $84,000, and C is$195,000 per year, which of the following best suits X’s investment plan in terms of capital allocation, given that his annualized hurdle rate is 20%?

1. Portfolio A
2. Portfolio B
3. Portfolio C

#### Solution

\begin{align*} \text{Portfolio A: } & \frac{95,000}{500,000}\times100=19\% \\ \text{Portfolio B: }& \frac{84,000}{400,000}\times100=21\% \\ \text{Portfolio C: }& \frac{195,000}{1,000,000}\times100=19.5\% \end{align*}

Portfolio B’s return exceeds the investor’s hurdle and, therefore, makes the best use of capital.

Reading 42: Measuring and Managing Market Risk

LOS 42 (k) Explain how risk measures may be used in capital allocation decisions.

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