11 votes

How to calculate Sharpe Ratio from $ returns?

Let's say your cumulative return series is $\{R_i \mid i=0,1,...,N-1\}$ of length $N$ days. There's 3 conventional ways to do this at this stage. You may convert the cumulative dollar return curve ...
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  • 5,062
10 votes
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What is the Sharpe ratio of two uncorrelated strategies, each with Sharpe ratio equal 1?

If we assume that by ensemble you mean an equally weighted portfolio of the two. We can express that portfolio as $$P = \frac{1}{2}x + \frac{1}{2}y$$ and the sharpe ratio of $P$, $S(P)$, will be $$\...
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10 votes

Maximum Sharpe portfolio (no short selling restrictions)

Let $R$ be a random vector of risky returns and let $r_f$ denote the risk free rate. Let vector of expected returns $\boldsymbol{\mu} = \operatorname{E}[R]$ and covariance matrix $\Sigma = \...
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  • 6,364
9 votes
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What is an acceptable Sharpe Ratio for a prop desk?

A Sharpe ratio of at least 1 in backtesting is a promising start, but that is just one of many statistics of interest. The Sharpe ratio measures return per unit volatility, i.e., return per unit risk....
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  • 475
9 votes
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Maximum Sharpe portfolio (no short selling restrictions)

There are two cases, where short sales are allowed: With riskless lending and borrowing and without. As mentioned in the comments, you just have to solve a linear system. With riskless lending and ...
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  • 2,996
8 votes
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How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?

To be consistent with the average daily returns that you specified, your first strategy would need to have a daily standard deviation of 31,749 USD and the second a standard deviation of 7,937 USD. ...
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  • 5,638
8 votes

Maximum Sharpe portfolio (no short selling restrictions)

To complement @skoestimeier's answer on the shortselling-allowed case, I provide a vectorised version. Using the original notation in my post (you may change $r$ to something like $r-r_f$, but this ...
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  • 921
7 votes
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Sharpe Ratio - my own calculation differs from Yahoo finance, Morningstar

Your approach of computation is not very standard. Specifically, you do not need to compute the annualized monthly return. One can compute the annualized Sharpe ratio from return sampled at any ...
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  • 799
7 votes

why does Cross Validation *not* solve Backtest overfitting?

If they publish information about all K trials, then you're right. But the author's point is that that's not typical practice. Typical practice is to not disclose that information, and it amounts to p-...
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  • 1,490
6 votes
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Difference between Sharpe Ratio and Information Ratio

Sharpe's 1966 equation had $R_b$ defined as the risk free rate. Looks like that was revised in 1994 to the 'reference benchmark', making the formulas essentially equivalent. If we refer to the ...
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  • 344
6 votes
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How to measure the Sharpe Ratio of a high frequency trading strategy?

Use daily P&L rather than return rate1. $$ Sharpe = \frac{\mu}{\sigma} $$ To annualize, multiply by the square root of the number of trading days in the year. For US equities, that would be 252. ...
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  • 9,649
6 votes
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How to test signifcance of a sharpe ratio

The answer above is not correct. Let's go by parts: Denote the mean of returns $\mu$. Denote the standard deviation of returns: $\sigma$. Therefore the sharpe ratio is: $$ SR = \frac{\mu-r_f}{\sigma} $...
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  • 6,820
5 votes

Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?

The correct answer is "arithmetic mean, because Bill Sharpe says so". He invented the thing, and he's pretty clear on which one he was looking at. If you use the geometric mean, which is lower the ...
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  • 51
5 votes

Sharpe Ratio : why the normalization factor?

If you're annualising your data with T it should always be the same, not changing with the length of your data. To demonstrate, annualising monthly returns, the ...
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5 votes

Sharpe ratio with leveraged ETFs

Probably missing something here but if $X$ has $E(X) = \mu$ and $variance(X) = \sigma^2$ then $2X$ has $E(2X) = 2 \mu, variance(2X) = 4\sigma^2$. Thus the sharp ratio defined as $\frac{\mu}{\sigma}$ ...
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  • 1,411
5 votes
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Is this a poorly written example, or could volatility in fact be negative?

You seem to use the term "volatility" to describe two very different quantities: (1) the diffusion coefficient of your SDE and (2) the standard deviation of the log-returns under your modelling ...
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  • 14k
5 votes
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Sharpe ratio: discrete or continuous returns?

For client reporting purposes, it is customary to use discrete returns. For backtesting, it pretty much make no difference.
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  • 10.9k
5 votes
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Sharpe Ratio of ETFs in R

try: library(PerformanceAnalytics) SharpeRatio.annualized(Returns, Rf = 0.05, scale = 252, geometric = TRUE)
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5 votes

Logic behind sharpe ratio

Another intuitive interpretation of the Sharpe ratio is as a signal-to-noise ratio: $$\frac{\mu}{\sigma}$$ where you compare the strength of the signal (= return) to the level of noise (= risk). The ...
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  • 27k
5 votes
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What is the industry standard way of calculating and annualizing performance metrics?

To give you an idea of industry standards for funds (although not hedge-fund specific), Morningstar and Trustnet both use monthly returns and annualize their data. See, for an example plucked at ...
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  • 1,356
5 votes
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Sharpe Ratio and Sortino Question: Standard practice

Theoretically, Sharpe should be the average of (compounded) excess returns divided by the volatility of the same. It was designed to measure the risk-reward preferring the risk asset to riskless. So ...
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  • 4,936
5 votes

What is stopping me from using high leverage on high Sharpe strategies?

Not sure if "3-4 Sharpe" indicates the value of the Sharpe ratio you're earning since such magnitude is meaningless without some benchmark to compare against, due to it being a purely ...
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  • 2,835
5 votes
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Do passive ETF fund managers care about profolio metric such sharpe ratios and sortino ratio?

Portfolio risk metrics matter a lot for all fund managers. Though certain type fund vehicles can have completely different sets of performance metrics. It's hard to imagine a Venture Fund analyzing ...
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5 votes

Do passive ETF fund managers care about profolio metric such sharpe ratios and sortino ratio?

The Sharpe ratio and the Sortino ratio are not under the control of the ETF managers, they will be equal (or very close) to the ratios for the Index that the ETF tracks. There is not much room for ...
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  • 9,617
4 votes

How do I calculate Sharpe ratio from P&L?

It is true that intraday/market-making strategies don't have a reasonable "return" metric. For this reason you can't characterize them with the Sharpe Ratio, which depends on a capital basis and how ...
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  • 233
4 votes

Sharpe Ratio : why the normalization factor?

I'll try to answer according to what I've read (and I hope mostly understood). Let's assume the mean of daily returns is 1%, and the standard deviation of daily returns is 1%. Then: $$ Sharpe = \...
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  • 767
4 votes

Sharpe Ratio : why the normalization factor?

The units of returns are 'per time', while the units of variance are also 'per time', thus the units of the Sharpe ratio are 'per square root time'. See section 2.2 of the Short Sharpe Course for a ...
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4 votes

How can risk-neutral pricing find the right price for securities if it doesn't account for risk premia?

The price of a derivative does not explicitly depend on the expected return of the underlying, however the price change or return of the derivative depends on the return of the underlying. Hence the ...
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  • 4,237
4 votes
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Simple Sharpe Ratio Question Related to Trading Strategy

First, you do not divide by the variance, but the standard deviation when calculating Sharpe ratios. Secondly, none of them are wrong, but $SR_1$ is the expected Sharpe ratio of the asset you are ...
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4 votes
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Sharpe Ratio, risk free rate

No, this is not the same. For example, consider the scenario $$ \begin{align*} r_A &= 10\% \quad\quad \sigma_A = 10\% \\ r_B &= 1.5\% \quad\quad \sigma_B = 1\% \\ \end{align*} $$ If $r_f=1\%$, ...
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  • 741

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