Question

The geometric average of −21%, 60%, and 55% is _________. What’s the arithmetic average?

An investment earns 30% the first year, earns 35% the second year, and loses 34% the third year. The total compound return over the 3 years was ______.

A portfolio with a 25% standard deviation generated a return of 17% last year when T-bills were paying 7.5%. This portfolio had a Sharpe ratio of ____.

You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. Your HPR was ____.

Answer 1

1). Geometric Mean = [(1 + r1) x (1 + r2) x .... x (1 + rN)]^1/N - 1

= [(1 - 0.21) x 1.60 x 1.55]^1/3 - 1

= [1.9592]^1/3 - 1 = 1.2513 - 1 = 0.2513, or 25.13%

Arithmetic Mean = [Ri] / n = [-21% + 60% + 55%] / 3 = 94% / 3 = 31.33%

2). Total Return = [(1 + r1) x (1 + r2) x .... x (1 + rN)] - 1

= [1.30 x 1.35 x (1 - 0.34)] - 1 = 1.1583 - 1 = 0.1583, or 15.83%

3). Sharpe Ratio = [E(r) - rF] / std. dev. = [17% - 7.5%] / 25% = 9.5% / 25% = 0.38

4). Dividend Yield = D1 / P0 = $3.50 / $50 = 0.07, or 7%

HPR = Dividend Yield + Capital Gains Yield = 7% + 4% = 11%