Jin-Hyun Nam

Jin-Hyun Nam Chapter 21.c. Investor Choice Investors do not normally allocate their entire investment on assets with the highest rate of return because risk is involved with this kind of action. Higher rates of return are commonly associated with greater risk and investors who are risk averse would not put themselves in this kind of situation. Figure 5.5.5.1 shows an investor’s indifference curve. Since the indifference curves are examining the volatility or risk as a bad and expected returns as a good, the investor’s indifference curves are upward-sloping. Return-Risk Tradeoff ReturnU2 U1Creturn2U0 A return1B risk1risk2Risk Figure 5.5.5.1 The Return-Risk Tradeoff. The indifference curves are upward-sloping if the expected return is a good and the risk or the volatility is seen as a bad. If the investor were to hold the expected return as return1, there would be a rise in risk associated with the return and point A would move to point B, which places the investor at a lower indifference curve from U1 to U2. Therefore, as the risk of the return rises from risk1 to risk2, the expected return also rises from return1 to return2. This will move the point B to point C to compensate for the added risk and keep the investor’s utility at U2. Investor Preferences toward Risk Risk averse investors prefer an asset which promises the same return at a higher stability. Therefore, as an asset’s instability of return increases, risk averse investors are compensated with a greater expected return to be equally well off, which would mean that they would be on the same indifference curve as they were before. Here, expected return is defined as the summed value of each possible rate of return weighted by its probability. For example, a return of 2 percent equals 100 while the utility of a return of 8 percent equals 300. The IBM stock will provide a return of 2 or 8 percent and that probability of this outcome is 50 percent. The expected return, E(Ri), is equal to 2(0.5) + 8(0.5) = 5. The expected utility is defined as the summed value of each possible utility weighted by its probability. The expected utility for this example is, E[U(Ri)] where it is equaled to 200, E[U(Ri)] = 100(0.5) + 300(0.5) = 200. In figure 5.5.5.2, total utility rises from 100 to 300 between the returns of 2 and 8 percent. Therefore, in order for it to reach a 200-unit increase in total utility as the return increases by 6 percent, the average utility must be at 5 percent – between 2 and 8 percent - because 200 is half the distance between 100 and 300 units of total utility. So as the height of the total utility curve at 5 percent exceeds the height of the straight-line chord at a return of 5 percent, this shows that the risk averse investor gets more utility from guaranteed return of 5 percent than from investing same thing which varies between 2 and 8 percent. Since a risk averse investor prefers a guaranteed return, it implies that the height of the total utility curve exceeds the height of the expected utility chord in this investment, U[E(Ri)] > E[U(Ri)]. Investor - Risk Averse Total utility, U U 300Z 225 200 A100 0528Return (%) per dollar invested in IBM stock, Ri Figure 5.5.5.2 Risk Averse Investor Risk averse investor’s total utility curve has an upward, but diminishing slope. This is because, for all returns between 2 and 8 percent, the height of the total utility curve exceeds the height of the expected utility chord and is therefore a risk averse investor. A risk neutral investor will be indifferent between a guaranteed return of 5 percent and investing in a risky IBM stock and expect a return of 5 percent. The total utility curve, 50, equals the height of the expected utility chord at the expected return of 5 percent because he has the same utility from a certain return as from an uncertain investment creating the same expected return. Investor – Risk Neutral Total utility, U U 80Z 50 A 20 0582Return (%) per dollar invested in IBM stock, Ri Figure 5.5.5.3 Risk Neutral Investor Risk neutral investor has a total utility curve that has an up-sloping straight line. The total utility curve and the expected utility curve have the same height between 2 and 8 percent and is therefore a neutral investor. A risk loving investor will prefer investing in the risky IBM stock which generates a 5 percent expected return over the guaranteed 5 percent return because his height of the investor’s total utility, 150, is less that the height of the expected utility, 175. A risk loving investor gets less utility from a guaranteed return than from an uncertain prospect creating the same expected return. Investor – Risk Loving Total utility, U U 325Z 175 150 A 25 0258Return (%) per dollar invested in IBM stock, Ri Figure 5.5.5.4 Risk Loving Investor Risk loving investor’s total utility curve has an upward-increasing slope. The height of the total utility curve does not exceed the height of the expected utility curve over the range of 2 and 8 percent and is therefore a risk lover.