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Questions tagged [sharpe-ratio]

Excess return per unit of deviation in return.

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25 views

Why isn't the Sharpe ratio risk free rate determined for each time period separately?

When calculating the Sharpe ratio why is the same risk free rate (90 day T-Bill) rather than the risk free rate for each individual period used?
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1answer
68 views

Portfolio Weight Sum and Negative Weights

I'm calculating the weights of 10 securities in a portfolio for a course project, with the objective of maximizing the sharpe ratio. I'm getting both positive and negative results for weights. The ...
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80 views

How to calculate “Differential Sharpe ratio”?

Instead of using the "sliding the time window" method of calculating the sharpe ratio under online framework, they've defined "differential sharpe ratio" as such But under equation 5, you can ...
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1answer
38 views

Calculation of Information Ratio

When calculating an information ratio, should the average of monthly returns be used or the cumulative monthly returns be used? Thanks!
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3answers
90 views

Calculating Sharpe Ratio with dynamic position sizing

I'm currently backtesting a mean reversion pairs trading strategy. However, instead of simple long or short trading signals, I'm using multiple "levels", where the further away the spread is from the ...
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4answers
225 views

sharpe ratio from regression

Suppose I run a regression of returns of an asset vs some signal. Is there a way to estimate Sharpe ratio of a strategy based on this signal from this regression? Assuming that signal is a real number ...
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1answer
55 views

How is breadth for Information Ratio Calculated

An alternative definition of the information Ratio (sharpe ratio) is: $IR = IC\sqrt{BR}$ I have been reading Grinold and Kahn. I have the following questions for calculating BR: Q1. If 500 stocks ...
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1answer
259 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 ...
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1answer
48 views

Sharpe Ratio with Stochastic Interest Rate?

All versions of the Sharpe ratio that I've seen seem to assume that the risk-free rate is constant, and the standard deviation of the excess return in the denominator simplifies to the standard ...
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1answer
66 views

Annualising Data

I have a 3 year performance track record of monthly returns. I am trying to calculate the Sortino Ratio, Information Ratio, Treynor index etc. In calculating the Sharpe Ratio I have multiplied the ...
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1answer
45 views

Multi year performance evaluations [closed]

first question here on StackExchange; I would value your help, I am on excel working with a 3 year / 36 month investment performance. I am calculating the Sharpe Ratio as follows; Cell KV32 = ...
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2answers
118 views

performance measure using pnl series

I have a time series of \$pnl of a strategy and nothing else. Can i use it to come up with some sort of a performance measure adjusted for risk? Is $$ \frac{average(\$pnl)} {sigma(\$pnl)}$$ ok to use ...
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138 views

Calculating Ex-Post Sharpe Ratio

I'm trying to calculate an Ex-Post Sharpe Ratio for my portfolio and I would appreciate verification I'm doing it correctly. I have my portfolio's daily returns in one column and my benchmark's ...
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43 views

How to calculate Sharpe Ratio and recovery factor for this data ? please help me im searching from 1 week

Suppose i have 5 closed trades like the following:- 1- 1 lot EUR/USD and got zero$ profit 2- 1 lot EUR/USD and got-6$ loss 3- 5 lot GBP/USD and got-45$ loss 4- 2 lot EUR/USD and got +20$ profit ...
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28 views

How do I prove that every point on the CML (capital market line) has the same RAP (risk-adjusted performance)?

Every point on the CML can be an optimal portfolio when combined with the according riskaversion factor (which creates a unique point on the CML where utility is maximized. But how do I proof that ...
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1answer
148 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 ...
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56 views

Definition request - Brownian Motion Characterised by Sharpe Ratio

What is the Stochastic Differential Equation for a "Brownian Motion Characterised by Sharpe Ratio"? I saw it in a paper ("Lessons from the Mortician: volatility modulation") and the authors do not ...
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0answers
81 views

Sharpe ratio for dynamic portfolio

I want to test the performance of my strategy with different rebalancing period. I'm struggle with calculating the overall performance on backtest results and making final conclusions. For example, ...
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1answer
167 views

Portfolio Allocation given Sharpe Ratio

If there are two portfolios with sharpe ratios of 1.2 and 0.5, what would be the allocation rationale. If the correlation between portfolios is: $a. 0 $ $b. 0.8 $ $c.-0.8 $ I see there is a ...
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1answer
868 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 ...
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1answer
499 views

maximize Sharpe ratio in portfolio optimization

I am trying to understand how to maximize Sharpe ratio in portfolio optimization. $\boxed{\begin{align}\max\>&\frac{r^Tx-r_f}{\sqrt{x^TQx}}\\ & \sum_i x_i = 1\\ & x_i\ge 0\end{align}}$ ...
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139 views

What do you optimize for? Sharpe ratio, profit factor, profit/drawdown, etc

In my experience, strategies perform best on OS (OutOfSample) data, when I optimize them for maximum Sharpe ratio (on InSample data) at the opposite extreme, when I optimize strategies for ...
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1answer
149 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$...
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76 views

Sharpe Ratio Calculation Best Practice

For Sharpe ratio formula : $SR(s) = \frac{(x_s - r)}{\sigma_s}$ where for the time period under evaluation : $x_s$ represents the average return of the portfolio $r$ represents average return of ...
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1answer
597 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 ...
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1answer
221 views

Many quants optimize sharpe ratios, sortino ratios, or anything of the form A/B. What about maximizing something of the form (AB)/(CD)?

The Sharpe ratio is defined as return/risk, generally as mean(ret)/sd(ret), where ret represents the data set of returns of an investment. However, I have seen other ratios that I also like. What I ...
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161 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. ...
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526 views

What is the CAPM implication for Sharpe Ratios?

Suppose a world where the CAPM holds, i.e. stocks with higher beta have higher expected returns. What would be in this world the implication for Sharpe Ratios? Would stocks with higher beta also have ...
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2answers
414 views

Calculating 10-year Sharpe ratio for a mutual fund in excel?

Probably a very simple question but here goes. I am looking to calculate the Sharpe ratio for some funds in excel (173 funds to be exact). The monthly returns I have are from January 2006 to December ...
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0answers
198 views

How to calculate semi-covariance matrix?

I am struggling find a reasonable approach to calculate semi-covariance matrix, focused on downside risk. I've went through several papers, Sortino's book and Estrada's research as well. However, I ...
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1answer
222 views

how is the sharpe ratio (or other risk/return measure) computed for a bond?

What is the industry norm to compute a sharpe ratio for a bond? For a stock one would typically take a time series of daily returns, compute the average daily return, compute the standard deviation ...
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1answer
80 views

How to correctly use SharpeRatio.annualized function with daily returns and proxy for daily risk free rate

I am not sure if am correctly using SharpeRatio.annualized function. I am passing following parameters (dailyRet, dailyRF, scale = 252), where dailyRet is an XTS type for daily returns, dailyRF is an ...
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1answer
115 views

Can someone please verify or disprove this Sharpe Ratio math logic for me

I want to start by stating a problem that I wanted to figure out initially so that this all ties in somehow. I initially wanted to figure out if individual securities in an efficient portfolio all ...
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1answer
130 views

Risk Compensation

I try to understand the different ways to compensate for risk. In the CAPM, when we plot the excess return against the risk, we find that portfolios of interest lie on the efficient frontier (i.e. ...
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1answer
167 views

Log returns: volatility, outperformance, Sharpe/information ratios

I have developed the habit of simply stating that a 21% return compared to a 10% benchmark return means that the outperformance was 10% (not 11%). So, treating the whole thing in a multiplicative way, ...
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5answers
295 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 ...
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1answer
261 views

Sharpe Ratio of ETFs in R

Suppose I want to calculate the Sharpe ratio given a risk free rate of 0.05 for a portfolio consisting of assets from 500 ETFs. How can I do so in R given the data I've collected thus far in my R code?...
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2answers
731 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, ...
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1answer
215 views

p-value of Sharpe Ratio Differences

I am trying to understand what was done in this study by Research Affiliates on the small cap anomaly. Looking at Table 1, how are the authors actually calculating the p-value? I have read that the ...
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1answer
171 views

Calculate Annualized Return / Annualized Sharpe From Portfolio

If I have a portfolio of stocks that I invest in and out of at different holding periods and different times of the year. How would one calculate the annualized returns and annualized sharpe ratio of ...
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1answer
1k views

How to maximize the Sharpe ratio given historical closing prices?

I have historical adjusted closing prices for $k$ stocks over $n$ days. I have a budget of $B$ dollars, and I'd like to choose allocations for each of the stocks, $a_{1:k}$, such that I maximize the ...
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2answers
65 views

If you have the (annualised) Sharpe ratios for some individual years, can you get the overall Sharpe ratio?

Suppose someone is doing some daily trading and tells you their annualised sharpe ratios for the following years: 2004: 0.7 2005: 1.2 2006: 1.1 2007: -0.2 Is it ...
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2answers
171 views

How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?

Let's say you have two trading strategies and all you're given is information about their average daily P&L and the Sharpe ratio of each strategy. Trading strategy A's daily average P&L is 10,...
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0answers
244 views

Differential Sortino Ratio

I'm attempting to optimize a reinforcement learning system to maximize risk adjusted returns. I have currently defined the reward as the differential Sharpe ratio at each step: the influence of the ...
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1answer
526 views

MPT Tangent Portfolio: Buck for the Bang Ratio

The $R_{TP}$ is the tangent portfolio return, but I don't understand the step regarding $\frac{dV(R)}{dw_n}$, you apply this, and how come it get rids of the summation?
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0answers
130 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 $
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2answers
540 views

Sharpe Ratio, risk free rate [closed]

when comparing the Sharpe Ratio (SR) of two different funds, does it make a difference, whether I use excess returs (returns - risk free rate) or returns (without dedcuting the risk free rate, ...
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1answer
167 views

Calculate Sharpe ratio for only one return [closed]

I have only one return for calculating sharp ratio. As you know, we should calculate standard deviation of returns and standard deviation of one item is 0. Suppose that the single return is 0.1 and ...
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0answers
114 views

Portfolio with several risky assets and one risk-free

Suppose we have $N$ risky assets $r_1$, $r_2$, ... , $r_N$ with a covariance matrix C. If we want to build a portfolio $\omega = (\omega_1, \ldots, \omega_N)^t$ (I loosely denote the portfolio with ...
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0answers
346 views

What is the Kelly Criterion for continuous probability case?

Given return of a portfolio or a single asset modeled as a continuous, but not necessarily gaussian, probability distribution, what's the Kelly criterion equation? I've heard that it's simply the ...