What fraction of financial wealth should be allocated to the US stock market for a person at retirement with no human capital?

Assignment 6

  1. Do Chapter 10 Problem 6 in BKM [Assume aA = 0 and aB = 0]
  2. Do Chapter 10 Problem 7 in BKM
  3. A mean-variance investor has relative risk aversion of 5. The investor chooses between a US stock market index and Treasury bills. Assume that the risk premium for the stock market is 6% and the standard deviation for the stock market is 20%.

a) What fraction of financial wealth should be allocated to the US stock market for a person at retirement with no human capital?

b) If the individual is an employee of the government (ph s = 0 and rrh = 0 05) and the present value of all future wages is 80% of the person’s total wealth portfolio at their current age. What fraction of financial wealth should be allocated to the US stock market currently?

c) If the individual is an investment banker (ph s = 0 6 and rrh = 0 15) and the present value of all future wages is 80% of the person’s total wealth portfolio at their current age. What fraction of financial wealth should be allocated to the US stock market currently?

d) Assume that there is no human capital remaining upon retirement. Should the fraction of financial wealth allocated to the stock market rise or fall as a government employee approaches retirement? Does this answer to this question change if the person is an investment banker instead? Briefly explain your answers.

  1. Compare 10 test portfolios using the CAPM model and 3-factor model. Please do not include the raw data in your solutions.

a) Download assignment6data.xls from the compass2g website.

b) Create a variable for the excess return of each portfolio as the difference between the return on the portfolio and the risk free rate (labeled rf).

c) Regress the portfolio excess return on the excess return of the market (labeled mkt_rf). There should be regression results for ten separate regressions.

d) What is the interpretation of the estimated constant (intercept) in the ten regressions?

e) For which portfolios (portid) is the constant statistically different from zero at a 5% level of significance and positive? For which of portfolios is the constant statistically different zero at a 5% level of significance and negative?

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f) According to the constants from the regressions of the excess return of the portfolio on the excess return of the market, does it appear that the constants are increasing or decreasing with the portfolio identifier (portid)? What trading strategy, if any, would you adopt to exploit this pattern?

g) Given your answer to part f), would you conclude that the market is efficient with regard to the information used to create these portfolios?

h) Regress the portfolio excess return on the excess return of the market, the SMB fac- tor, and the HML factor. Again, there should be regression results for another ten separate regressions.

i) For which portfolios (portid) is the constant statistically different from zero at a 5% level of significance and positive? For which of these portfolios (portid) is the constant statistically different from zero at a 5% level of significance and negative? What trading strategy, if any, would you adopt to exploit this pattern?

j) Assume that SMB and HML represent for systematic risk factors. Given your answer to part i) would you conclude that the market is efficient with regard to the information used to create these portfolios?

k) According to the other coefficients from the regressions of the excess return of the portfolio on the excess return of the market, SMB, and HML, which portfolios (portid) have a statistically significant loading (different from zero) on the value factor?

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