Questions tagged [sharpe-ratio]

Excess return per unit of deviation in return.

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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
980 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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396 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
116 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
130 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
177 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
413 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
612 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
438 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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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
432 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
304 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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3k 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
118 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
352 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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470 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
1k 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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207 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
831 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
246 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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174 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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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 ...
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1answer
314 views

Simple Sharpe Ratio Question Related to Trading Strategy

Given a price vector $(p_1,p_2,...,p_n)$ for some stock, then the corresponding return at $k$th day is described by $$ R_k = \frac{p_{k+1} - p_k}{p_k} $$ On the other hand, let $W_k$ be wealth at day ...
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1answer
130 views

How can risk-neutral pricing find the right price for securities if it doesn't account for risk premia?

I'm confused as to how a method that values securities purely on their expected return works in the real world if it doesn't take into account the fact that investors demand a higher return for ...
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1answer
699 views

Should the Sharpe ratio of a portfolio change when it is leveraged?

I am trying to understand why the Sharpe ratio changes (increases) when I simulate leveraging my portfolio by multiplying all the time series of daily returns by a leverage factor (e.g. 5). I ...
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601 views

when calculating sharpe ratio of a backtest, do you use the historical risk-free rate or the current one?

Say I'm running a few backtests, say 1980-now, 2000-now and 2010-2015. When I'm calculating the Sharpe ratio of these backtests, do I use the risk-free rates associated with those time periods? or ...
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453 views

Sharpe ratio: discrete or continuous returns?

The Sharpe ratio is known as $$SR=\frac{\mu-r_f}{\sigma}$$ Are these values calculated from discrete or continuously compounded returns?
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1k 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?
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volatilty and Sharpe Ratio of long-short portfolio

What is the proper way to calculate volatility for the long short portfolio? if calculated in a standard way the offsetting positions are driving it down. How about Sharpe Ratio? that has an impact ...
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1answer
109 views

How do I loop through all the stocks and find the 10 stocks with the highest Sharpe ratio using R program?

I am recently doing a project, which I need to apply Sharpe ratio to all the stocks. How do I loop through all the stocks and find the 10 stocks with the highest Sharpe ratio using R program? Thanks a ...
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3answers
18k 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: ...
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1answer
281 views

Is this a poorly written example, or could volatility in fact be negative?

I'm self-studying and I encountered the following example. It seems to suggest that volatility is negative in this example. I was under the impression that volatility can never be negative, both from ...
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193 views

Sharpe ratio highest amongst efficient portfolios?

I have a hard time understanding why the sharpe ratio corrresponding to the efficient portfolios is the highest possible. In my book, it states that the sharpe ratio of the efficient portfolios is ...
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1answer
115 views

Can I deduce a portfolio is inefficient by compare is Sharpe ratio to the on the one the tangent portfolio?

If I have a portfolio with a Sharpe ratio lower than the Sharpe ratio of the tangent portfolio, can I conclude something about whether or not it is efficient? If so, how/why?
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1answer
124 views

Adding negative EV position to portfolio for diversification?

Say I have a portfolio of expected return $10\%$ and volatility $20\%$. If I have another asset that is either one of: Negatively correlated Positively correlated Uncorrelated With negative expected ...
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1answer
442 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!...
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1answer
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Geometric means, standard deviation, and sharpe ratios

I have 3 related questions: a) I've seen formulas for GM and GS which eithier do, or do not, involve taking the exponent. Which is right? i.e. for GM I've seen both mean(ln(1+rt)) and exp(mean(ln(1+...
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1answer
161 views

Having Difficulty With Sharpe Ratio and Optimal Portfolio

I have begun by using such equations as: By finding the $Rp$ and $\sigma p$ with the weighted values, and then I followed the equation using a value of $.02$ for the fixed asset, $rf$, but this comes ...
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1answer
2k views

Calculate excess returns for Sharpe Ratio with today's or past risk free rate of return?

I am struggling with the calculation of the Sharpe ratio. I am wondering whether to calculate the daily excess returns with today's risk free rate of return or the risk free rates corresponding to the ...
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1answer
904 views

Calculate total risk [closed]

I have a question regarding how the risk is calculated, if I have only the returns. I think the risk premium (rp) is just the average of the returns and the sharpe ratio is the risk premium divided by ...
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4answers
1k views

Evaluation of portfolio other than Sharpe Ratio

Is Sharpe ratio always the best way to evaluate a portfolio? I'm not really sure what this potential interview question wants me to answer. I have read that Sharpe ratio essentially explains how ...
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1answer
237 views

How to calculate Sharpe Ratio if there are gaps in returns?

I see a lot of examples, like "We hold long position during whole year, then we calculate daily sharpe ratio and multiply it by SQRT(252) to get the annual one". This example makes sense for me. ...
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1answer
389 views

Why does the Sharpe ratio not change when the strategy is leveraged?

It has been correctly stated that the Sharpe ratio of a strategy does not change when it is leveraged. I understand Eric's point that leveraging by $n$ multiplies both the return $x$ and volatility $\...
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1answer
951 views

How to compare Sharpe Ratios of different investment strategies (holding periods)

I am doing the momentum analysis and am trying to see, what strategy (based on trading frequency) yields the highest Sharpe ratio for different investment amounts. The trading frequencies I use are ...
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1answer
234 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 ...
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52 views

Do I calculate weights of assets correctly?

I solved attached question but I am not sure whether I did part a and c correctly. Is there a way to calculate weights of A and B by just knowing their standard deviation and correlation's value?
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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: ...