Questions tagged [sharpe-ratio]

Excess return per unit of deviation in return.

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1 answer
53 views

Question about marginal risk contribution / portfolio volatility decomposition

I am trying to understand the rule where you add a new asset to a portfolio if its Sharpe ratio is greater than the product of the portfolio sharpe ratio and the correlation between the portfolio and ...
0 votes
1 answer
201 views

efficient frontiers are equal

I created 3 different efficient frontiers with 3 different risk factors(sharpe ratio, ulcer performance index and serenity ratio) and I wanted to find both MSR and GMV(and their equivalent for the ...
0 votes
1 answer
112 views

Sharpe ratio 1 and probability to lose money

I came across the following interview problem and I am looking for a possible solution. We have a strategy with risk free return 0 and sharpe ratio 1. What is the probability to lose money over four ...
0 votes
0 answers
45 views

Formal Sharpe Ratio Calculation

Would appreciate clarity from senior quants on the correct way to calculate sharpe Back in the zero interest rates days, I saw some senior quants would calculate sharpe ratio as avg(pnl)/std(pnl) and ...
2 votes
1 answer
407 views

How to Maximize Portfolio Sharpe Ratio using Lagrange Multipliers in a Factor Model

I've come across the notes of the 2003 lecture "Advanced Lecture on Mathematical Science and Information Science I: Optimization in Finance" by Reha H. Tutuncu. It describes on page 62 in ...
0 votes
0 answers
34 views

Sharpe ratios (and other risk-adjusted metrics) on Terminal wealth (long-horizon payoffs)

I'm exploring financial simulations with bootstrapped returns (TxNBoot) to calculate long-horizon returns. Terminal wealth (e.g compounded returns at T) is a vector of payoffs (NBootx1), typically ...
2 votes
1 answer
288 views

how to calculate the Sharpe ratio based on a list of trades, with space between them?

First, there are a few things I'm not clear about, like what the 'risk free' return is.. is there even such a thing in trading? or how to handle inactive days, etc. Let's assume I have a period of 30 ...
0 votes
1 answer
127 views

Portfolio Optimization with ETFs and Futures

I am looking to perform portfolio optimization with a single ETF (or two) and a VIX futures (with the possibility of adding an additional hedging instrument). Here are some features of my portfolio ...
-1 votes
1 answer
85 views

About the problem of maximizing Sharpe ratio [closed]

Regarding this problem, is this equivalent to optimize the standard mean variance portfolio and then comparing the Sharpe ratio of all the portfolio along the efficient frontier? Edit: Instead of ...
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?
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 ...
4 votes
2 answers
355 views

Sharpe ratio with CVaR for denominator and different investor utility functions

I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper ...
1 vote
1 answer
279 views

Optimising returns weighted by Sharpe ratio in the context of Supervised Learning

In the Kaggle Jane Street market prediction competition we are put in a Supervised Learning Framework to deal with 'trade opportunities'. That is, we are given instances of previous trade ...
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0 answers
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Deriving probability of hitting stop loss given annual return and Sharpe

Suppose I have a strategy with a mean return and defined Sharpe. Given a preset stop loss, I want to calculate the probability of the stop being hit. In the example below I use the following ...
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0 answers
75 views

Supervised metric including beta?

I am working in a supervised ML framework. I'd like to define one metric to evaluate a strategy. Naturally I was initially enclined towards overall returns or sharpe ratio. I'd like to implement a ...
1 vote
1 answer
95 views

Calculating Ex Post Sharp Ratio's for decile portfolios

Dear Stack community, I hereby would like to ask what the correct calculation is for calculating Ex Post Sharp Ratio's. If I am correct, I already know that I am supposed to divide the average excess ...
0 votes
0 answers
67 views

Constraints in a Mean-Variance Optimization Case

Might be a repeat question, feel free to close if it is. I am trying to perform a mean-variance optimization (maximizing the Sharpe ratio) for lets say 5 assets. Besides the weights of the assets ...
0 votes
0 answers
56 views

Adjusting the p-value of a strategy for number of parameters

Let's say I have some metric and I'm trying to evaluate whether it's predictive with respect to returns. I plan to only take trades where the value of the metric is above a certain threshold, such ...
0 votes
0 answers
66 views

Determine expected geometric return from Sharpe ratio

I'm trying to calculate the expected annual geometric return, given that I'm provided with an annual Sharpe ratio (0.5), the yield on a 3-month T-Bill (5%) (using this yield as a proxy for the risk-...
3 votes
1 answer
343 views

Proof that Sharpe ratio of the benchmark is related to the maximal information ratio and Sharpe ratio

I understand the economic logic behind it, that the active portfolio with the highest information ratio will also have the highest Sharpe ratio, but I can't see how $SR_B^2 = SR_P^2 - IR^2 $
64 votes
8 answers
109k views

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.
0 votes
0 answers
101 views

Relationship between holding time and sharpe ratio

Let's say, for simplicity, I have a long-only portfolio $P$ that consists solely of equity. The average holding period for each asset is $n$ days. Are there research papers or theorems that ...
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 ...
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?
4 votes
1 answer
944 views

How to derive the CAPM from maximizing the Sharpe ratio?

I know how to derive at the CAPM from a microeconomic foundation. In a recent University course I stumbled over a slide that derived the CAPM solely from the Sharpe ratio: I cant come up with that ...
1 vote
1 answer
380 views

How does one show that the Sharpe Ratio is closely related to the t-statistic of the mean differential return?

I see it being mentioned in many places, such as here, and even here. How should I interpret it? Suppose I have an array of signals, I, and returns of those signals, R Then my regression is R = a + BI ...
0 votes
0 answers
54 views

Does imbalance not impact returns-calculation weighing when calculating the Sharpe Ratio of an equity Long-Short strategy?

I'm calculating the Sharpe Ratio for a simple equity long-short strategy (short stock S and use proceeds to buy stock L). Obviously this is self-financing. In "https://quant.stackexchange.com/...
2 votes
0 answers
99 views

Squared Sharpe Ratio - Fama and French

I am investigating various versions of nested and nonnested Fama and French factor models. Performance of the models is compared on the basis of Squared Sharpe Ratios. Bariallas et al. (2020, JFQA) ...
0 votes
1 answer
213 views

Finding latest market price of market portfolio according to No Arbitrage

In Excel, I have the monthly stock price data for the past few years for Asset A and Asset B. I have calculated the monthly returns, mean returns, variances, and standard deviations for both stocks as ...
3 votes
1 answer
462 views

Mixing Max Drawdown and Sharpe Ratio in a single utility function : is there a standard approach?

We know that 2 strategies can give the same Sharpe Ratio, but with different Maximum Drawdown. I computed myself these 2 strategies having the same cumulative return and SR, but with considerably ...
1 vote
1 answer
206 views

Figuring out how TradingView calculates the Sharpe ratio [closed]

This is the simplest backtest I've come up with, yet I can't figure out how TradingView has calculated the Sharpe ratio to be 0.577. I've set the risk_free_rate=0. Is it possible to extract the ...
1 vote
1 answer
265 views

Why isn't the Sharpe Ratio computed on the cumulative return rather than return mean? [closed]

I have learnt that the Sharpe ratio is a measure of the annualized return rate mean over the annualised standard deviation of return rate distribution. I also learnt that when compounding, the mean of ...
0 votes
0 answers
63 views

alternatives of sharpe's ratio with respect to maximum-drawdown(mdd)

Given a window, expected return divided by standard deviation is sharpe's ratio. But I want to form another figure for mdd-adjusted return. mdd divided by expected return can be suggested but it seems ...
1 vote
0 answers
337 views

Derivation Treynor-Black model

In the treynor-black model the assumption is that markets are not fully optimal and it is possible to achieve additional alpha on top of the market portfolio. After a mean-variance optimization ...
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33 views

Is there a formal notion of a "reward measure"?

A risk measure, as defined in the Wikipedia page, is a function that maps random variables to real numbers and satisfies the normalized, translative, and monotone properties. There are many other ...
2 votes
2 answers
729 views

How to annualize Sharpe Ratio if monthly returns are serially correlated? Calculation of autocorrelations

I am looking at a data set of 60 monthly returns (last 5 years) and want to calculate an annualized Sharpe Ratio. The usual way of doing this is to calculate the monthly Sharpe Ratio first, and then ...
0 votes
1 answer
765 views

long short portfolio sharpe ratio

What is the proper way to caluclate sharpe ratio for the long short portfolio? When I calculate daily return with no cost, I use this formula: (return for long k.mean()+ (-1)*(return for short k.mean()...
4 votes
1 answer
530 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 \...
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: $$\...
1 vote
1 answer
823 views

How to derive the sharpe ratio for an intraday strategy

I have an intraday strategy, which will place 0-5 trades for each intraday trading session. (Note that some days it will not place any trades out). The average duration of a trade is around 33 minutes....
0 votes
1 answer
704 views

What can we say about the probability a strategy losing money in a year if it has an annualized Sharpe of say 2?

If we imposed the restriction that the strategy is not skewed, then using Chebyshev's Inequality I can show that the probability of it losing money in a year is less than 12.5%. Let $X$ be the yearly ...
0 votes
0 answers
321 views

How to annualize sharpe ratio using quarterly data?

Say I have quarterly returns data for a stock. I am currently calculating rolling Sharpe ratios using an eight-quarter forward window. So for example, say I have quarterly returns data starting in ...
0 votes
2 answers
220 views

Why not calculate Kelly using semivariance? As w Sortino

Kelly is calculated as mu / sigma^2. If we remove our highest performing returns from our calculations this actually increases our Kelly leverage, which does not make sense to me. A less profitable ...
3 votes
3 answers
3k views

mean-variance optimization === max sharpe ratio portfolio?

Noobie here. I just wanna ask a simple question: in the context of portfolio optimization, is Mean-Variance optimization the same as the max sharpe ratio portfolio?
0 votes
1 answer
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Are there better performance measures for mean-reverting vs trend-following trading strategies?

The Sharpe ratio is often used as measure to assess risk-adjusted returns of trading strategies. However, there are also other measures that can be used to assess risk-adjusted returns like the ...
0 votes
0 answers
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Relationship between Sharpe Ratio and Investment Horizon in a theoretical IID return world

In his paper, "The Statistics of Sharpe Ratio", Andrew Lo writes "hence, the ratio will increase as the square root of q, making a longer horizon investment seem more attractive. This ...
1 vote
1 answer
527 views

What are "df", "t", and "p" in these sharpe ratio related estimates?

I am looking at some sharpe ratio related estimates and have not seen Sharpe stats broken down this way before. I don't know what is meant by df, t, and p. Can someone explain that to me? Thank you!...
1 vote
1 answer
109 views

Difference between Treynor ratio and market premium

The definition of Treynor ratio is given by $$ T = \frac{r_i-r_f}{\beta_i}, $$ where $r_i$ is the portfolio $i$'s return, $r_f$ is the risk-free rate and $\beta_i$ is the portfolio $i$'s beta. I am ...
1 vote
0 answers
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I am comparing two assets Rolling 10 Year Sharpe Ratios. I want to know what percentage increase in Sharpe Ratio is meaningful?

If Asset A is having 35% higher Sharpe Ratio than Asset B is that significant? Or should I consider that only if Asset A is having 50% higher Sharpe Ratio than Asset B.
1 vote
1 answer
287 views

Confidence in Sharpe ratio given performance

Suppose I have a strategy that I believe has a Sharpe ratio of X - not the Sharpe ratio of the backtest (this can be absolutely determined), but the ratio I expect it will actually take on over the ...

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