APU MATH530 2021 March Week 3 Discussion Latest

MATH530 Applied Statistics

Week 3 Discussion

Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in "boom" state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a "boom" state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1--and is.

State of economy            Probability          Market Return  Gold Return

Boom    0.15        25%        (-30%)

Moderate Growth           0.35        20%        (-9%)

Week Growth   0.25        5%          35%

No Growth         0.25        (-14%)   50%

Question #1: Compute the expected return for each alternative. Based on their expected returns, would you rather invest your money in the stock market or in gold? Why?

Next, compute the standard deviation of the return associated with an investment in gold and the standard deviation of the return associated with an investment in the market.

Question #2: Now, given their expected returns and the standard deviations of their returns, would you rather invest in gold or the stock market?  Why?

Questions 1 and 2 above can be answered using the material in Chapter 5 of our textbook. This last question goes well beyond those topics and is a real challenge. Suppose that in addition to investing in gold or in the stock market you could invest in a portfolio consisting of a combination of gold and the market. In particular, suppose that you could invest in a portfolio made up of 40% stock and 60% gold.

Question #3: Which of the 3 options would you prefer-(1) invest in gold alone, (2) invest in the market alone, or (3) invest 40% in the market and 60% in gold?  Why?