Questions tagged [sharpe-ratio]

Excess return per unit of deviation in return.

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64 votes
8 answers
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How to annualize Sharpe Ratio?

If I know the daily returns of my portfolio, I need to multiply the Sharpe Ratio by $\sqrt{252}$ to have it annualized. I don't understand why that is.
David's user avatar
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30 votes
11 answers
25k views

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

What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances?
Kelly's user avatar
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29 votes
5 answers
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Should Sharpe ratio be computed using log returns or relative returns?

I am trying to reconcile some research with some published values of 'Sharpe ratio', and would like to know the 'standard' method for computing the same: Based on daily returns? Monthly? Weekly? ...
shabbychef's user avatar
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21 votes
6 answers
29k views

How high of a Sharpe ratio is implausibly high for a low-frequency equity strategy?

I am looking to convince someone that an annualized Sharpe Ratio of 7 is 'extremely high' for a low frequency (daily rebalancing, say) long-short technical strategy on U.S. equities. I was hoping for ...
shabbychef's user avatar
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20 votes
2 answers
15k views

Kelly criterion and Sharpe ratio

Whats the relationship between the Kelly criterion and the Sharpe ratio? $$ f=\frac{p(b+1)-1}{b} $$ where $f$ is a percentage of how much capital to place on a bet, $p$ is the probability of success,...
jessica's user avatar
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20 votes
2 answers
1k views

How do you correct Max Draw-Down for auto-correlation?

When returns are auto-correlated, calculating a Sharpe ratio := $\frac {mean(x)}{\sqrt{var(x)}}$, (where $x$ are the returns) is complicated, but basically solved (see, e.g. Lo (2005)). Without the ...
Paul H. Lasky's user avatar
19 votes
4 answers
11k views

Sharpe ratio and leverage

Does leverage affect the Sharpe ratio? If my Sharpe is 2 at no leverage, does it change, fall by half say, at a different leverage?
ZoStone's user avatar
  • 199
15 votes
1 answer
741 views

How does one measure the effect of latency on potential returns?

I am looking to evaluate the hypothetical advantage one trading system has over another in terms of the possible returns given their latency. Irene Aldridge wrote a piece (How Profitable Are High-...
Jonathan Evans's user avatar
14 votes
2 answers
5k views

Normality assumption in Sharpe ratio

I have read that the Sharpe ratio imposes a normality assumption, but I fail to see how. Standard deviation is statistic for any type of distribution. Anyone have any ideas?
user6997's user avatar
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14 votes
1 answer
707 views

Can we use White's reality check to compare two Sharpe ratios?

I read a paper from Ledoit and Wolf that proposes a method to compare two Sharpe ratios and a paper from White that proposes a method to compare $n$ trading rules. My question is: Can we use White's ...
rich's user avatar
  • 141
13 votes
2 answers
5k views

Computing the Sharpe Ratio

The building blocks of the Sharpe ratio—expected returns and volatilities—are unknown quantities that must be estimated statistically and are subject to estimation error. The main problem I have is ...
user4796's user avatar
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13 votes
1 answer
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Intuitive explanation of the Hansen-Jagannathan bound

The Hansen-Jagannathan bound states that the maximum Sharpe ratio of a portfolio can't exceed the ratio of the standard deviation of a stochastic discount factor to its mean. I more or less understand ...
Bob Jansen's user avatar
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12 votes
4 answers
1k views

Is this a common variation of sharpe ratio?

As an aside on his answer on another question Freddy said: Sharpe ratio is an often cited metric, though I do not like it too much because you are penalized for out-sized positive returns while I ...
Darren Cook's user avatar
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12 votes
2 answers
15k views

How to calculate Sharpe Ratio from $ returns?

I have a pairs strategy that I am trying to calculate the sharpe ratio for. Currently I am using python for my analysis and calculation. I have a dataframe that contains the cumulative returns in $'s ...
jod51's user avatar
  • 141
10 votes
1 answer
2k views

What is the average Sharpe ratio of volatility arbitrage funds?

Where can I get data on performance metrics for volatility arbitrage funds? I am trying to compare the Sharpe ratio of my strategy to those of the major players.
Alan's user avatar
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10 votes
1 answer
1k views

Forget Kelly, forget fractional sizing. Where is the general theory?

I am struggling to find a general theory of position sizing. Help! The literature is all about fractional position sizing, but that's just one of the innumerable strategies. What about all the other ...
elemolotiv's user avatar
9 votes
2 answers
12k views

How do I calculate Sharpe ratio from P&L?

Say I have a market-making strategy that trades intraday. I start with a flat position and finish flat too. I end up with a daily P&L $p_{today}$. Over a year of trading I get $\vec{p} = (p_1,\...
statquant's user avatar
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8 votes
3 answers
6k views

Maximum Sharpe portfolio (no short selling restrictions)

Suppose we have $n$ assets whose expected return vector is $r$ and is positive, and whose covariance matrix is $\Sigma$. Is there a closed form or quasi closed form (like the eigenvector of a matrix ...
Vim's user avatar
  • 903
8 votes
3 answers
5k views

What is an acceptable Sharpe Ratio for a prop desk?

What should be the value of a Sharpe Ratio for an intraday quantitative strategy to be accepted by a bank or hedge fund's prop desk? Let's assume the returns are daily changes in account equity, close ...
Sergey Bushmanov's user avatar
8 votes
2 answers
5k views

Annualized Sharpe Ratio calculation

I'm trying to replicate the annualized Sharpe ratio of an buy-and-hold strategy for the Dow Jones Industrial Average index for a period consisting of multiple years. I got the daily DJIA (closing) ...
Wildman's user avatar
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8 votes
1 answer
246 views

Propagation of Errors of Sharpe Ratio

Looking at Opdyke, J.D., Comparing Sharpe Ratios: So Where are the P-Values?, page 22 (Appendix A) an application is given for the Propagation of Errors formula on a ratio of two random variables: $$\...
oronimbus's user avatar
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7 votes
2 answers
6k views

How to define the objective function for a custom optimization problem?

I would like to find the allocations that would minimize some user-defined metric (Sortino, minimum drawdown, etc) for a portfolio of assets. How would one go about formulating the objective ...
user1234440's user avatar
7 votes
2 answers
3k views

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

Given two uncorrelated strategies, each with a Sharpe ratio of 1, what is the of Sharpe ratio of the ensemble?
pvstrln's user avatar
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7 votes
2 answers
920 views

how to choose top n assets?

I have m assets, and have estimated their future returns and covariance matrix. I would like to invest in an evenly weighted n product basket from this universe, where 0<n<m. How do i find the ...
user847663's user avatar
7 votes
2 answers
3k views

How should I compute the Sharpe Ratio for mid-frequency pair trading strategy?

I have a pair trading strategy with positions that last 3-5 days and trades 2-3 times a month. By design, all the trades are profitable until the cointegration is broken. Should I calculate the ...
Victor's user avatar
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7 votes
1 answer
446 views

Alternative relative performance measure to Sharpe ratio for non-IID return

The Sharpe ratio is often used to compare the relative performance of portfolios despite its IID-assumption for the returns being violated. I can find ample warnings about the consequences of ...
David Newton's user avatar
7 votes
1 answer
407 views

Significance testing of average returns from Sharpe ratio

I'm aware that one way to do significance testing on a strategy is based on the sampling distribution of its Sharpe (see, e.g., Lo, 2002 and Opdyke, 2008). However, it appears to me that there's ...
Powerfool's user avatar
  • 101
6 votes
3 answers
2k views

Sharpe Ratio : why the normalization factor?

I try to understand why a $\sqrt{252}$ normalization factor is useful for Sharpe Ratio: Let's compute the Sharpe Ratio for this imaginary portfolio, for various sampling periods: ...
Basj's user avatar
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6 votes
1 answer
592 views

why does Cross Validation *not* solve Backtest overfitting?

In this famous paper, Bailey and De Prado discard Cross Validation as tool to check for Backtest overfitting, on the ground that it is just an holdout method: ... If we apply the holdout method ...
elemolotiv's user avatar
6 votes
2 answers
2k views

Calculate Daily Returns for Sharpe Ratio

For the purposes of Sharpe ratio, I calculate a trading strategy's daily returns using realized P/L only: $$ \frac{K(t + 1) - K(t)}{K(t)}, $$ where $K(t)$ is the cash balance after market close on day ...
Tom Tucker's user avatar
6 votes
1 answer
784 views

What is the relation between Relative Risk Aversion and Market Price of Risk

If we assume that the preferences of investors in a market aggregate to display the following utility function $$u(W)=\dfrac{1}{1-\gamma}W^{1-\gamma},\quad \gamma>0,\quad \gamma\neq1$$ then from$...
user33475's user avatar
  • 137
6 votes
1 answer
2k views

Alpha vs. Sharpe Ratio

What are the main differences between a strategy's Sharpe ratio, and its alpha based on the Fame French factors? Does it make sense to evaluate them both in a thesis?
John's user avatar
  • 349
5 votes
2 answers
596 views

Question about adding new investment A to portfolio B

I've found a ton of sources that mention the classic rule of "If the Sharpe ratio of the new asset is greater than the Sharpe ratio of the existing portfolio times the correlation of the existing ...
jauyjad's user avatar
  • 51
5 votes
1 answer
3k views

How to measure the Sharpe Ratio of a high frequency trading strategy?

The Sharpe Ratio is defined as Sharpe ratio = (Mean portfolio return − Risk-free rate)/Standard deviation of portfolio return. Unfortunately, this does not make ...
Scott Skiles's user avatar
5 votes
3 answers
3k views

How can I find the portfolio with maximum Sharpe Ratio - Using Lagrange Multipliers

In Markowitz' portfolio theory we can construct portfolios with the minimum variance for a given expected return (or vice versa). Across expected risks, this traces out the well-known efficient ...
Zac's user avatar
  • 207
5 votes
3 answers
2k views

Bootstrapping Sharpe Ratios

A similar question to this was asked here: How do i test the significance of Sharpe ratio of a strategy using bootstrap I have bootstrapped the original time series (using block bootstrapping) and ...
Bazman's user avatar
  • 879
5 votes
2 answers
4k views

mean variance optimization vs max sharpe ratio

I keep reading/hearing that the results from mean-var optimization is max Sharpe ratio. It seems making sense if you fix either target return or target risk, but in general, it doesn't seems right, ...
starx's user avatar
  • 51
5 votes
0 answers
409 views

Bayesian strategy selection

I have N strategies/signals that I would like to allocate to. I want to estimate an estimate of future performance based off of recent realized performance (momentum of strategies per se - e.g. ...
Michael's user avatar
  • 490
4 votes
5 answers
1k views

Logic behind sharpe ratio

I have a confusion regarding how the sharpe ratio is derived. My question is why the denominator contains the standard deviation of returns of portfolio? I mean why did someone came to this conclusion ...
uchiha.itachi's user avatar
4 votes
2 answers
14k views

Sharpe Ratio, annualized monthly returns vs annual returns vs annual rolling returns?

I would like to calculate the Yearly Sharpe Ratio on MSCI World index I have monthly values of the index that falls back up to Jan/1970, hence about: 44 years, 528 months In order to calculate ...
Marco Demaio's user avatar
4 votes
4 answers
2k views

Sharpe ratio in days with no open positions

Should I include or not the days a strategy has no open positions (thus no returns) in the Sharpe ratio calculation?
Victor's user avatar
  • 1,200
4 votes
2 answers
463 views

How is someone's Sharpe ratio recorded and communicated?

When I read about, say, some hedge fund wanting people with such-and-such Sharpe ratio, how is that ratio recorded and communicated to the interested party? I mean, do people just take it on faith ...
Dmitri Nesteruk's user avatar
4 votes
2 answers
3k views

Difference between Sharpe Ratio and Information Ratio

I am finding it difficult to understand the difference between the sharpe ratio and the information ratio and the relationship between the two, and cannot find a decent reference that breaks it down ...
WeakLearner's user avatar
4 votes
2 answers
2k views

Sharpe Ratio Formula

In calculating Sharpe Ratio, I have come across a variety of equations that are similar but differ in wordings. I am curious to know which one is used within best practice. Here are all the different ...
Jack Armstrong's user avatar
4 votes
1 answer
3k views

What is the industry standard way of calculating and annualizing performance metrics?

Say I am looking at a performance report for a hedge fund manager who trades mostly equities, and they provide me a list of monthly returns for the past 5 years. What is the industry standard way to ...
Edward Yu's user avatar
  • 247
4 votes
1 answer
378 views

Sharpe ratio with leveraged ETFs

There has been a discussion about how leverage affects Sharpe Ratios, but not in the context of leveraged ETFs (such as 2x or 3x). I'm just wondering how leveraged ETFs, if at all, change the ...
Ed S.'s user avatar
  • 41
4 votes
1 answer
529 views

If returns are correlated, are Sharpe ratios correlated?

Suppose we have two correlated return series: $$a \sim N(\mu_a,\sigma_a^2)$$ $$b \sim N(\mu_b,\sigma_b^2)$$ $$correl(a,b)=\rho$$ The sample Sharpe ratios of the two series, after $t$ samples for $t \...
elemolotiv's user avatar
4 votes
1 answer
1k views

Is scaled Sharpe ratio a t-statistic?

I was just reading Quantitative Trading: How to Build Your Own Algorithmic Trading Business and it suggests annualizing Sharpe ratio in order to compare performance of strategies: $$\text{Annualized ...
spacemonkey's user avatar
4 votes
3 answers
26k views

What value should the risk free monthly return rate be (Sharpe ratio calculation)?

In calculating an annualized Sharpe ratio using monthly returns, what is commonly used as the value for the risk free rate? I am using this formula: ...
shell's user avatar
  • 151
4 votes
1 answer
679 views

How is the Sharpe Ratio presented in fund profiles usually calculated?

To compare my stock portfolio generator with managed funds performance, I want to calculate the Sharpe Ratio of my historic portfolios with the numbers found on the fund company web sites or in ...
TvdH's user avatar
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