$2.$ Exercises for Evaluating Trading Strategies: Performance Measures

For each of the following exercises, consider the hedge fund index data provided and evaluate the performance $($abstracting here from the potential biases in the data$).$

$2\mathrm{.}1.$ Performance measures. For each hedge fund style, calculate and interpret the following performance measures

a$.$ Annualized arithmetic average return

b$.$ Annualized geometric average return

c$.$ Annualized volatility of excess returns

d$.$ Annualized Sharpe ratio

e$.$ Market beta

f$.$ Annualized alpha to the market

g$.$ Annualized Information ratio

h$.$ Maximum drawdown

i$.$ Skewness of monthly excess returns

j$.$ Excess kurtosis of monthly excess returns

$2\mathrm{.}2.$ Cumulative return and drawdown. Make the following plots for Global Macro Hedge Fund index

a$.$ The cumulative return

b$.$ The drawdown

$2\mathrm{.}3.$ Factor models. For Equity Long$/$Short$,$ run two regressions: $($i$)$ a univariate regression of the hedge fund index$$s excess return on market excess return; and $($ii$)$ a multivariate regression on the market, size, value, and momentum factors.

a$.$ Interpret the loadings on the different factors. What do we learn of the investment style?

b$.$ Compare the multivariate alpha with the alpha from the univariate market regression. Discuss

the difference in interpretation between the univariate vs$.$ multivariate alphas.

$2\mathrm{.}4.$ Illiquidity and stale prices. For Convertible Bond Arbitrage excess returns, compare:

a$.$ The beta in a monthly univariate regression on the market$$s excess return.

b$.$ The beta in a univariate regression on the market using $3-$month excess returns. $($To compute $3-$

month excess returns in a simplified way, add $3$ monthly excess returns. The regression coefficients can still be estimated by running the regression monthly, i$.$e$.,$ with overlapping data, but, in this case, t$-$statistics need to be adjusted if you were to consider these$).$

c$.$ The sum of betas in a monthly regression on the market, the $1-$month lagged market, and the $2-$ month lagged market $($all excess returns$).$

How do I calculate each of these using excel?