Part 2 Tkm0844 11e Im Ch08
Chapter 8
Risk and Return: Capital Market Theory
8-1. To find the expected return from James Fromholtz’s investment opportunity, we will use equation 7-3:
where i indexes the various states of nature that are possible. We can picture the states of nature for James’s opportunity as:
Despite the symmetrical appearance of the graph, the outcomes are not symmetrical: There are many more outcomes that are positive than negative. Only the 100% return (probability 5%) is negative; 95% of the weight of the distribution is positive. We could still have a negative expected return if the magnitude of the negative return were large enough to overwhelm the other possible outcomes. However, that won’t happen here, since the +100% return, which also has a 5% chance of occurring, “balances” our one negative outcome.
A. Applying equation 7-3 to our probability distribution of returns, we have:
E(r) (0.05) (100%) (0.45) (35%) (0.45) (5%) (0.05) (100%) 18%. We can see these calculations in the spreadsheet below. Note that the probabilities must sum to 1(100%).
B. The expected return for this investment is positive, as it will be for all investments on an ex ante basis—people wouldn’t invest if they expected to lose money! (This is what distinguishes investing from gambling.) However, just because the expected return is positive does not mean that I would necessarily invest. The expected return must be sufficient to compensate me for the risk that I bear. Knowing that there is a possibility of a negative outcome is not sufficient as a measure of risk. Therefore, I can’t say whether or not I’d invest in this opportunity—I’d need more information. Part of what I’d need to know we will find out in Problem 8-2 (but again, that won’t be enough!).
8-2. To find the standard deviation of the probability distribution given in Problem 8-1, we will use equation 7-5:
where I indexes the various states of nature. For James Fromholtz’s opportunity, we have:
We can
Risk and Return: Capital Market Theory
8-1. To find the expected return from James Fromholtz’s investment opportunity, we will use equation 7-3:
where i indexes the various states of nature that are possible. We can picture the states of nature for James’s opportunity as:
Despite the symmetrical appearance of the graph, the outcomes are not symmetrical: There are many more outcomes that are positive than negative. Only the 100% return (probability 5%) is negative; 95% of the weight of the distribution is positive. We could still have a negative expected return if the magnitude of the negative return were large enough to overwhelm the other possible outcomes. However, that won’t happen here, since the +100% return, which also has a 5% chance of occurring, “balances” our one negative outcome.
A. Applying equation 7-3 to our probability distribution of returns, we have:
E(r) (0.05) (100%) (0.45) (35%) (0.45) (5%) (0.05) (100%) 18%. We can see these calculations in the spreadsheet below. Note that the probabilities must sum to 1(100%).
B. The expected return for this investment is positive, as it will be for all investments on an ex ante basis—people wouldn’t invest if they expected to lose money! (This is what distinguishes investing from gambling.) However, just because the expected return is positive does not mean that I would necessarily invest. The expected return must be sufficient to compensate me for the risk that I bear. Knowing that there is a possibility of a negative outcome is not sufficient as a measure of risk. Therefore, I can’t say whether or not I’d invest in this opportunity—I’d need more information. Part of what I’d need to know we will find out in Problem 8-2 (but again, that won’t be enough!).
8-2. To find the standard deviation of the probability distribution given in Problem 8-1, we will use equation 7-5:
where I indexes the various states of nature. For James Fromholtz’s opportunity, we have:
We can