Decision-Tree Analysis The optimal payoff is $0, which would occur under scenario D1, O1.

The EMV for the first decision, which is the decision not to evacuate, is the highest. The reason for this is that the costs associated with the hurricane hitting the area, and the area not being evacuated, are very high. If the hurricane does not hit, the do nothing option has the lowest cost, but because of the risk of the hurricane hitting at least partially, the EMV for this option is the highest. The EMV for the second decision is the second-highest. This is a recommended evacuation, which incurs some costs, but a lower dollar value than the cost of a full evacuation. There are some savings, but the EMV is still fairly high.

The lowest EMV comes with a mandatory evacuation. This has the highest base incurred cost, but the likelihood that the hurricane will miss the area is low. What that means is that because the hurricane has a high likelihood of hitting the area, the mandatory evacuation will be the least costly overall in terms of EMV. The savings from avoiding an evacuation only make sense when the risk to the community is low.

My decision is the mandatory evacuation. In the real world, it might make sense to wait until more is known about the hurricane -- it is still in the Caribbean, after all. But given the information presented, the likelihood of at least a partial hit is 80%. Knowing that, an evacuation makes the most sense, because the costs of any hit are high if there are still people in the area. The community does not save much by avoiding an evacuation, relative to the cost associated with still having people in the area when the hurricane hits.

Question 2.

b. The best decision depends on a lot of factors, such as the investor's cash needs and risk tolerance. In the real world, nobody should invest in risky stocks if they need the money in just one year. But since we know nothing about the investor, we can only use EMV to guide the decision. In this case, the best decision based on EMV is the portfolio of all risky stocks. The EMV of this option is $860.

c. The riskiest option, of course, has the highest standard deviation of any portfolio among the six options. This is why risk tolerance is important. Changing the risk free rate of return does not affect the EMV decision, because it only affects the return on the risk free portfolio. None of the top EMV options contain risk-free securities. To look at the risk-free rate in isolation, it would need to be 9% in order to change the decision. At 9% or higher, the portfolio with 100% risk free would return better. In practice, it is unusual for stock markets to...

However, we know that markets do have down years, so there are instances where risk free securities outperform equity markets. The investor must be aware that if the risk free rate is better than the expected return on an equity portfolio, it will have the better EMV.
The starting value of the account is not relevant, because the EMVs reflect a percentage return on the starting value.

d. 1. The best decision, customer factors notwithstanding, is to accept the current predictions and opt for the high-risk portfolio. The reason is that this has the highest EMV. If the risk-free rate today is 3%, it is highly unlikely that this will average over 9% for the year, unless you are in a third world country having a bad year. So the fixed income return is unlikely to change materially over the course of the year, and variability in equity returns has already been taken into account in the calculation. The highest EMV is $860 with the all high-risk portfolio.

d. 2. There is, of course, another factor that has not yet been taken into account, and that is risk-adjusted rate of return. The highest EMV comes from the highest-risk portfolio. However, the EMV of a split stock portfolio is $830 and the EMV of an all-safe stock portfolio is $800. The standard deviation of the safe stock returns is much lower than the standard deviation of the risky stock returns. As such, most investors being risk-averse, would probably prefer the EMV of $800 with low volatility over the EMV of $860 or even $830 and high or medium-volatility. On a risk-adjusted basis, the $800 EMV from the all-safe portfolio is probably the best outcome, though the numbers are available to prove that.

d. 3. Changing the amount of initial investment did not change the decision. Every calculation is a percentage return on the initial investment, so the relationship between the EMV and the initial return is a constant. The risk-free rate, however, did results in changes to the final decision. Changing the risk free rate affects the risk free portfolio return. Lowering the risk free rate does not change anything about the calculation, but increasing it does. As noted above, when the risk free rate is 9%, the risk-free portfolio is now returning a greater yield than the risky portfolio, which returns 8.6% At 8.6%, the EMV of the risk-free portfolio is equal to the expected return of the risky portfolio. Once the risk is taken into account, it is apparent that even if the risk free rate is below that of equity returns (say, 7%), it is probably superior on a risk-adjusted basis because there is no volatility at all in the risk-free return, by definition. The…