Read the article Diversification Return, Portfolio Rebalancing and the Commodity Return Puzzle, by Scott Willenbrock published in 2011 in the Financial Analyst Journal, 67 (4), pp. 42-49. You are not expected to understand all elements, particularly all the formulae in this article.

Answer each of the following questions briefly. The total number of marks available is 20. Each question is worth two marks.

Consider a portfolio consisting of two assets that are initially equally weighted. The simple returns of the first asset are 25 percent, -20 percent, whereas the simple returns of the second asset are the reverse: -20 percent, 25 percent. Each asset has a vanishing geometric average return over the two holding periods. If the portfolio is rebalanced to equal weights after the first holding period, how ever, it has a gain of 5.06 percent, which corresponds to a geometric average return of 2.5 percent. This return is a diversification return.

4. Validate the statement that the rebalanced portfolio returns 5.06% and the geometric average return is 2.5%. What are the weights of each asset in the portfolio at the end of each period? (2 marks)

The reading states (3rd paragraph page 44)

The diversification return is the difference between the geometric average returns of both a rebalanced portfolio of volatile assets and a rebal anced portfolio of hypothetical assets with the same weights and geometric average returns as the true assets but zero volatility. An appropriate name for the geometric average return of the hypothetical portfolio might be the strategic return because it depends on only the geometric average returns of the assets and their weights in the portfolio. Thus, for a rebalanced portfolio,

Diversification return = Geometric average return - Strategic return.

5. Using the data located at Aswath Damodaran's website

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html

or

http://www.stern.nyu.edu/~adamodar/pc/datasets/histretSP.xls ,

4

compute the Strategic Return, Diversification Return and 50/50 Portfolio Return as per Table 1 in Willenbrock's paper. (2 marks)

6. Interpret the returns of question 5. (2 marks)

7.