# Questions about Sharpe Ratio calculation

1. Let's say I have daily returns. Don't they depend on the risk per trade I am using? Obviously, if I'm risking 2% of equity per trade returns will be drastically different than when I'm using 10%? So if I have a strategy I have to assume a certain % risk per trade in order to calculate Sharpe? Wouldn't it be too easy to manipulate Sharpe by just changing this parameter?

2. I'm going to use one of these bad boys for risk-free rate here.

https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield

But which one should I use? Given that I'm working with daily returns, not yearly.

1. When inputting daily returns in Sharpe formula should they be compounded or not? Like if I start with \$100 in equity should every daily return be based on \$100 in equity?

## 1 Answer

Question1: I think you're confused on what you're actually measuring. Don't think about this in terms of trades, think about it in terms of the total value of your portfolio. At day 1 you have 100 dollars, tomorrow you have 110, 2 days from now 115 and a week from now it's back to 105. How many trades you made during that period, how big those positions are or even how much cash you have is irrelevant. The time series of those portfolio values (100, 110, 115.... 105) is from where you calculate your standard deviation and average return to get your Sharpe Ratio.

Question 2: Even if you're working with daily returns and measure the daily standard deviation it's probably a good idea to transform those into yearly measures (in fact you need to do so in order to calculate your Sharpe ratio). Just take $$1-(1+r)^{252}$$, where r is your average daily return calculated in question 1, to get your average yearly return and $$\sigma_ {daily} * \sqrt{252}$$ to get your volatlity as a yearly measure. The interest rates you found are already measured yearly. the correct rate to use is the theoretical risk free rate, so none of them really, but the 10-year rate should be fine for your purposes.

Question 3: Again, not sure what you mean. Do you mean if you should use the geometric or arithmetic mean when finding your average rate of return? I would use the geometric but I'm sure you'll be able to find people with differing opinions.

• 1. 252 for markets that don't trade 365 days a year? 2. by compouning or not I mean difference betwen: Let's say I make 3% per trade on average. Compunded: 100 103 103*1.03 103*1.03*1.03 not compouned 103 103 103 103 So compounded would change capital base on every new day and calculate return off it. Non-compunded would start with $100 every day. The daily returns are different in the two cases. 100 103 – lachimba Jun 19 '20 at 13:32 • Yes, 252 is usually used as the number of trading days in a year – Oscar Jun 19 '20 at 13:34 • by compouning or not I mean difference betwen: Let's say I make 3% per trade on average. Compunded: 100 103 103*1.03 103*1.03*1.03 not compouned 103 103 103 103 So compounded would change capital base on every new day and calculate return off it. Non-compunded would start with$100 every day. The daily returns are different for the two cases. – lachimba Jun 19 '20 at 13:37
• Sorry it's confusing. I guess best way I can put it is do we change our equity on every new day as it fluctuates up and down with new trades or we start every day with hypothetical \$100? – lachimba Jun 19 '20 at 13:40
• It doesn't matter. 3% return is 3% return regardless if it's acting on 100 dollars or 200 dollars – Oscar Jun 19 '20 at 13:41