# Questions tagged [sharpe-ratio]

Excess return per unit of deviation in return.

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### Robust Sharpe ratio

The denominator of the Sharpe ratio is sample portfolio volatility, $\sigma_p$, which is the square root of portfolio variance based on the quadratic squared loss, L2. Alternatives for the denominator ...
253 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 ...
39 views

### Sharpe ratio of strategy exploiting correlations that vary by time interval

The Epps effect "is the phenomenon that the empirical correlation between the returns of two different stocks decreases with the length of the interval for which the price changes are measured" (...
84 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 ...
92 views

### T-bond of what maturity to use as risk-free rate when calculating excess return?

I am comparing different asset classes in order to estimate the expected return and the risk of a portfolio. I have historical data (adjusted close price) for my asset classes for the last 5 years ...
51 views

### step by step calculation of the sharpe ratio

I am trying to calculate the Sharpe ratio. Suppose I have: $$x_t = \alpha + \beta y_{t} + \epsilon_{t}$$ $$E[x_{t}] = \alpha + \beta E[y_{t}]$$ $$var[x_{t}] = \beta^2var[y_t] + \sigma^2$$ The ...
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### Is there any way to compare portfolios created using sharpe optimization model?

I created different portfolios using sharpe portfolio optimization model and I want to know is there any way to compare those portfolios before actually investing in them?
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### Annualizing Sharpe Ratio using small time frames

I have coded a strategy that works 5m time frame. I know you multiply it by 252 but i am using 5m or sometimes 1h time frame. Which number do i have to chose to multiply? There are 72576 five minutes ...
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### Sharpe Ratio and Sortino Question: Standard practice

For Sharpe ratio calculation, I have seen several variations for the denominator; either the standard deviation of portfolio returns or standard deviation of excess returns. Is there an accepted ...
32 views

### Relation between Sharpe ratio and amount of capital

In the book Quantitative trading by Ernest P. Chan, in one of the example we compute the Sharpe ratio of long-short strategy and one step perplexes me: In column L, compute the net returns for ...
148 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?
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### 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 ...
48 views

### Risk-free rate in the Sharpe ratio

Let's say I have data stemming from date $t_1$ to date $t_2$, I have the annualized return each day during those two dates. Therefore I know the expected return and the standard deviation of the ...
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### Why not to maximize Sharpe Ratio directly when computing optimal allocation of an order?

I was reading the following paper of Engle about balancing transaction costs performance and risk: https://www.nber.org/papers/w12165.pdf He deals with finding the optimal placement of the child ...
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### How to annualize sharpe with non-continuous trading days

I want to calculate annual sharpe of my tradingsignal. I assume risk free rate is zero, so my sharpe is return to risk, not excess return. My trading signal is binary on/off for different trading ...
45 views

### Calculation of the risk free rate

For portfolio management I need the risk-free to compute the sharpe ratio. I would like the use to rate on the 3 month treasury bill from the US. https://fred.stlouisfed.org/series/TB3MS#0 The ...
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### Given multiple strategies with their ER, volatility, how would I calculate the combined Sharpe?

Without knowing the actual daily returns, I have a table something like this: ...
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### Sharpe Ratio and interest rate

The Sharpe ratio is calculated as the ratio between the return and the volatility. Now, when I have a trading strategy that requires to be invested sometimes and to be flat other times, I assume 0% ...
92 views

### Sharpe Ratio - Linear Homogeneous

In the book "Portfolio Construction and Risk Budgeting" of Sherer, there is an excercise with the following prompt: "Use matrix algebra to find the maximum Sharpe ratio portfolio. Show that the ...
101 views

### Geometric Sharpe ratio

I'm computing different metrics for mutual fund performance. I want to use classic Sharpe ratio, but I also got to know there is geometric Sharpe ratio. Unfortunately I didn't find enough info about ...
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### Deriving Single Index Model (Market Model)

is the return of the stock of observation is the return of the reference market is the regression coefficient between the observed stock and the reference market is the regression intercept between ...
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### Distribution of the Information Ratio // Mean and Variance Product

We are investigating the distribtuion of the information ratio. However, instead of using the original information ratio defined as \begin{equation} IR=\frac{E(r_1)-E(r_2)}{\sqrt{Var(r_1-r_2)}}, \end{...
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### sharp ratio/sortino ratio for options portfolio

I am thinking that the sharp ratio is not a valid performance metric for a long/short options book, because options are inherently nonlinear and the standard deviation simply cannot correctly capture ...
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### How/Why Markowitz model is normatitive while CAPM positive?

I've tried economic books but they only give this "should/is" explanations and I still cannot see how it applies to MPT. On the other hand, almost every paper and book gives these adjectives before ...
41 views

### Calculate best share based on return of investement and standard devation (Without risk free rate)

I have a microeconomics task in investment analysis. How do you pick the best share based on return of investment and standard deviations? The task is like this: 3 shares: Share A: 10% ROI & 20% ...
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### Sharpe testing in R

My goal test: The statistical significance of the difference in Sharpe ratio between funds A and B. My data: I have daily prices from January 23 2008 until 10th of April 2019 (n = 2818 observations). ...
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### Sharpe Ratio - How do I calculate my risk free rate from daily yield data?

I am trying to compute a Sharpe ratio for a portfolio spanning over 20 years. I have daily data for the portfolio, as well as the yield of CH10Yr (10 year bond in Switzerland, downloaded from Thomson ...
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### No-arbitrage and the sharpe ratio?

I'm reading a paper and it says that in a no-arbitrage market the sharpe ratio is the same for all bonds. I'm guessing that a difference in two bonds sharpe ratios would open the possibility of ...
107 views

### Modified Sharpe ratio

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 ...
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### Calculating Ex-ante Sharpe Ratio in multi-period setting

I have built a return process $\{x_t, t = 1,\dots,T\}$ for an asset. Suppose I have generated $K$ sample paths $\{x_t^j, t=1,\dots,T\}, j=1,\dots,K$. I think of two ways to compute the Sharpe ratio. ...
63 views

### Can I calculate Sharpe ratio by running over many samples?

I have an algorithm that I am backtesting 200 times. It trades over 200 trading days per iteration. My sharpe ratio is calculated as follows: ...
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### Compare ex-post Sharpe ratio of multiple portfolios?

Say I want to compare the Sharpe ratio of two portfolios, is it necessary to look at the excess return? Or can you just compare their average return divided by their standard deviation? So basically, ...
148 views

### Risk-return ratio using ML default probability

I have access to a very large bond database (>20m rows) where 50% of the set are matured bonds for which a dummy variable identifies whether the bond defaulted or not. The remaining 50% are 'live' ...
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### Which performance evaluation measure to assess “Connectedness Matrix” based porfolios?

1. Question Which performance evaluation measure would be best to assess the portfolios built on 'connectedness matrix'? The connectedness matrix is the concept introduced in the academic paper "...
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### Alpha decay for strong vs weak signals

Assuming you are computing alpha decay similarly to shown here (e.g., exponential decay of the information ratio with lagged signals). I'm wondering whether it is preferable to treat strong vs weak ...
2k 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 ...
129 views

### A positive Sharpe ratio when portfolio loses money, can that happen or bug in my code?

I'm having a trouble calculating (annualized from daily performance) Sharpe ratio, even though I've read some related posts here. Say I have a daily performance, for example: $$[1.15, 1.2, 0.7]$$ ...
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### Another variation of the 'Sharpe ratio' in CVaR-based portfolio optimization?

Question What is the ratio S(p) shown below? Do we have a name for it like 'Sharpe ratio'? The ratio above is introduced in the academic paper Optimal portfolio selection in a Value-at-Risk framework ...
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### Is the sharpe ratio calculated taking the standard deviation of the portfolio or of the excess return?

Does the formula consider the standard deviation of the excess return: $$\frac{𝑟−𝑟_𝑓}{𝜎{(𝑟−𝑟_𝑓)}}$$ or that of the return: $$\frac{𝑟−𝑟_𝑓}{𝜎{(𝑟)}}$$
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### Simulated Sharpe Ratio Calculation for Leveraged Portfolio

I've written some VBA code to simulate the effect of borrowing money, investing it, and repaying the loan daily. PseduoCode: Start with a portfolio value of P = 1 Each day borrow P, invest 2*P, ...
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### Maximum Sharpe Ratio Portfolio

Conceptually, what are the drawbacks / unforeseen risks of running a portfolio whose weight are derived from what would have maximised the sharpe ratio over the previous time period (last 30 days) ?
2k 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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### 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 ...
51 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!
284 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 ...
527 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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### 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 ...
917 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 ...