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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 = \...
Matthew Gunn's user avatar
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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 ...
madilyn's user avatar
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11 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 ...
skoestlmeier's user avatar
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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 $$\...
Quantifeye's user avatar
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 ...
Vim's user avatar
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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. ...
Chris Taylor's user avatar
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8 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-...
Jase's user avatar
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7 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. ...
chrisaycock's user avatar
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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 ...
vonjd's user avatar
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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} $...
phdstudent's user avatar
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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.
Helin's user avatar
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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 ...
Quantuple's user avatar
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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 ...
m.a.i.'s user avatar
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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)
DataAdventurer's user avatar
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 $...
Matthew Gunn's user avatar
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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 ...
Tim Wilding's user avatar
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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 ...
demully's user avatar
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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 ...
develarist's user avatar
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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 ...
Desmond830's user avatar
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 ...
nbbo2's user avatar
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5 votes
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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)}\\ &= \...
Matthew Gunn's user avatar
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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 ...
oronimbus's user avatar
  • 1,896
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 ...
steveo'america's user avatar
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 ...
Forgottenscience's user avatar
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 ...
Kiwiakos's user avatar
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4 votes

What is the Sharpe ratio of two uncorrelated strategies, each with Sharpe ratio equal 1?

Of course, it depends on the weights of your 'ensemble'. The optimal combination will have the following Sharpe ratio: $$ S_{opt} = \sqrt{S_1^2+S_2^2} $$ i.e. $S_{opt} = \sqrt{2} \approx 1.414$ in ...
Johannes Gerer's user avatar
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 $r_f=1\%$, ...
msitt's user avatar
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4 votes
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Risk Compensation

A linear relationship between expected returns and covariance with a risk factor is a necessary consequence of a linear asset pricing function In theory, a CAPM relationship can be derived when a ...
Matthew Gunn's user avatar
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4 votes
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How can I find the portfolio with maximum Sharpe Ratio - Using Lagrange Multipliers

The trick is in the transformation of the constraints used to solve the optimisation problem. This can be seen in the definition of the set $\chi^+$ in the two lines following equation 5.4 of Tütüncü. ...
Tim Wilding's user avatar
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4 votes
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What is the relation between Relative Risk Aversion and Market Price of Risk

In most economic models the risk aversion coefficient is definitely related to the equity premium. Assuming utility is CRRA (as you mention): \begin{equation} U(C_t) = \frac{C_t^{1-\gamma}}{1-\...
phdstudent's user avatar
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