# Sharpe testing in R

My goal test: The statistical significance of the difference in Sharpe ratio between funds A and B.

My data: I have daily prices from January 23 2008 until 10th of April 2019 (n = 2818 observations). I upload an excel sheet to r with prices of fund A in column 1 and prices of fund B in column 2.

R Code: I run the following code

## Run Sharpe testing (asymptotic hac)
x = SR_for_r[,1]
y = SR_for_r[,2]
ctr = list(type = 1, hac = TRUE)
out = sharpeTesting(x, y, control = ctr)
print(out)

## Run Sharpe testing (circular bootstrap)
x = SR_for_r[,1]
y = SR_for_r[,2]
set.seed(1234)
ctr = list(type = 2, nBoot = 1000, bBoot = 3)
out = sharpeTesting(x, y, control = ctr)
print(out)


My questions

1) Should I have fund prices, rate of return, or excess returns in columns 1 and 2 in the datasheet I import to R?

2) Should I use HAC standard errors only or use circular bootstrap to test the statistical significance of the Sharpe ratio difference?

3) How can I interpret the output from the test?

4) Does anyone know of an article of someone who have tested the statistical significance of the Sharpe ratio difference between two funds?

My Sources: The R code comes from here: https://rdrr.io/cran/PeerPerformance/man/sharpeTesting.html

Unless you're doing this as a purely educational exercise, it looks like you may be overcomplicating things.

Sharpe ratios follow a student's t distribution. You can thus use standard approaches to test hypotheses or create confidence intervals for each Sharpe estimate.