12
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 = \...
- 6,924
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 ...
- 5,231
11
votes
Accepted
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 ...
- 2,906
10
votes
Accepted
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 $$\...
- 373
9
votes
Accepted
What is an acceptable Sharpe Ratio for a prop desk?
A Sharpe ratio of at least 1 in backtesting is a promising start, but that is just one of many statistics of interest. The Sharpe ratio measures return per unit volatility, i.e., return per unit risk....
- 415
9
votes
Maximum Sharpe portfolio (no short selling restrictions)
To complement @skoestimeier's answer on the shortselling-allowed case, I provide a vectorised version. Using the original notation in my post (you may change $r$ to something like $r-r_f$, but this ...
- 893
8
votes
Accepted
How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?
To be consistent with the average daily returns that you specified, your first strategy would need to have a daily standard deviation of 31,749 USD and the second a standard deviation of 7,937 USD.
...
- 5,891
7
votes
why does Cross Validation *not* solve Backtest overfitting?
If they publish information about all K trials, then you're right. But the author's point is that that's not typical practice. Typical practice is to not disclose that information, and it amounts to p-...
- 1,500
6
votes
Logic behind sharpe ratio
Another intuitive interpretation of the Sharpe ratio is as a signal-to-noise ratio: $$\frac{\mu}{\sigma}$$ where you compare the strength of the signal (= return) to the level of noise (= risk).
The ...
- 27.3k
6
votes
Accepted
How to measure the Sharpe Ratio of a high frequency trading strategy?
Use daily P&L rather than return rate1.
$$ Sharpe = \frac{\mu}{\sigma} $$
To annualize, multiply by the square root of the number of trading days in the year. For US equities, that would be 252.
...
- 9,797
6
votes
Accepted
How to test signifcance of a sharpe ratio
The answer above is not correct.
Let's go by parts:
Denote the mean of returns $\mu$. Denote the standard deviation of returns: $\sigma$.
Therefore the sharpe ratio is:
$$ SR = \frac{\mu-r_f}{\sigma} $...
- 8,022
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 ...
- 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 ...
- 581
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 $\frac{\mu}{\sigma}$ ...
- 1,558
5
votes
Accepted
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 ...
- 14.5k
5
votes
Accepted
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.
- 11.4k
5
votes
Accepted
Sharpe Ratio of ETFs in R
try:
library(PerformanceAnalytics)
SharpeRatio.annualized(Returns, Rf = 0.05, scale = 252, geometric = TRUE)
- 646
5
votes
Logic behind sharpe ratio
People compute the Sharpe ratio because it has some useful properties.
If you increase the leverage of a strategy, the Sharpe ratio remains the same
Let $R$ be the return to some strategy. And let $...
- 6,924
5
votes
Accepted
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 ...
- 1,396
5
votes
Accepted
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 ...
- 5,041
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 ...
- 2,980
5
votes
Accepted
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 ...
- 86
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 ...
- 10.9k
5
votes
Accepted
Is this quadratic form the Sharpe ratio?
Perhaps this is helpful. Look at my answer to a related question to follow my notation better.
$$ \begin{align*}a &\equiv \sum_i \sum_j V_{ij} \mu_i \quad \quad \text{(in Merton paper)}\\
&= \...
- 6,924
5
votes
Question about adding new investment A to portfolio B
The proposition is intuitive but the proof of this is not so straight forward in my opinion. The paper Benhamou & Guez (2021), Computation of the marginal contribution of Sharpe
ratio and other ...
- 1,841
4
votes
Sharpe Ratio : why the normalization factor?
The units of returns are 'per time', while the units of variance are also 'per time', thus the units of the Sharpe ratio are 'per square root time'. See section 2.2 of the Short Sharpe Course for a ...
- 547
4
votes
Sharpe Ratio : why the normalization factor?
I'll try to answer according to what I've read (and I hope mostly understood).
Let's assume the mean of daily returns is 1%, and the standard deviation of daily returns is 1%. Then:
$$ Sharpe = \...
- 777
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 ...
- 4,307
4
votes
Accepted
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 ...
- 717
4
votes
Accepted
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 $r_f=1\%$,
...
- 741
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