【正文】
iversified investors hold portfolios that have already eliminated all of a firm’s specific risk, but investors cannot eliminate market risk. The equilibrium market price of each firm’s shares in the portfolio is such that expected returns only pensate investors for holding market risk, as embodied in a firm’s beta. As such, riskmanagement activities by the firm are irrelevant in the sense that they are unable to add value. These activities may reduce total risk, but diversified investors have already done so by eliminating all of the specific risk. Hence, risk management activities will not increase the market price of the firm’s shares. Shapiro and Titman (1998) argue that, since financial instruments are fairly priced, and pensate investors for market risk only, hedging risk through financial instruments is, at best, a zero net present value (NPV) activity. In the worst scenario, risk management may actually be value reducing, since it may be a costly activity in terms of time and resources. Risk management irrelevance can be analysed as follows. Consider the value of the firm as the sum of the discounted value of expected future cashflows. That is, if the firm is expecting cashflows of X1 in year i, and the firm discounts at a cost of capital r, then firm value V is given by: V 1=X 1/(1+r) + X 2/(1+r)^2+…(1) The cost of capital (or the investors’ required return) includes an element for market risk. The firm’s risk management activities reduce total risk, but this will not affect the market risk. Therefore, the firm’s beta will be unchanged, and hence the cost of capital r will remain the same. Having demonstrated how risk management may be (at best) an irrelevant activity, Sheperd and Titman (1998) proceed to rescue risk management by showing that it can have an effect on firm value. They argue that total risk does matter, through its effects on the cashflows. A high level of total risk may increase expectations of financial distress, hence reducing the expected cashflows, and reducing firm value. Risk management aimed at reducing total risk, although not affecting the discount rate, may increase expected cashflows, which would be value increasing.Furthermore, a firm’s managers have an incentive to engage in risk management, even if this is not value increasing. A single firm’s financial distress may not be of much concern for a welldiversified investor. However, it could be disastrous for the management of that firm, in terms of loss of employment and reputation. It may be argued that management has a private discount rate which reflects total risk, and hence exceeds the social discount rate r. Since the firm is valued in the market using r, the management would have a lower private valuation of the firm than the market. Risk management could then be viewed as management’s attempts to increase their private valuation towards the market valuation.Should we adjust the discount rate?Shimko (2001) argues that welldiversified investors do not exist. Therefore, the NPV method of investment appraisal may be flawed, since it uses a discount rate that only reflects market risk. He proposes an adjustment to the NPV method in order to take account of total risk. His riskadjusted present value (RPV) method attacks the problem by adjusting the discount rate. Shimko’s RPV approach is derived as follows.Consider a one period investment project with present value V 1 at time 0 (this is the amount that the investor is prepared to pay at time 0, and is defined as cash capital). The time 1 cashflow provided by the project is a normally distributed random variable with mean μ 1 and standard deviation σ 1. Shimko assumes that the cashflow is not correlated with any market risk factors. The riskfree rate is r.The investor requires a return on his/her cash capital and his/her risk capital. Risk capital is the maximum amount that the investor might lose on the project over the year. In order to derive risk capital, the firm must define a “worst case” time 1 cashflow, W1=μ1? is, the worst case cashflow is z standard deviations below the mean. The present value of the worst case cashflow is W 0=W1/ (1+r). Hence, risk capital =V0?W0.The expected capital gain over the year is: μ1V=r*V0+k*(V0W0) (2)The lefthand side shows that the expected capital gain is the expected time 1 value (that is, the mean) minus the initial cash investment. The righthand side partitions this expected gain into the return on cash capital r*V0 plus the return on risk capital k*