11

Here are couple references. Especially the first link to Andy Lo's paper contains a list of Sharpe ratios of popular mutual and hedge funds: The Statistics of Sharpe Ratios Dow Jones Credit Suisse Hedge Fund Index Generalized Sharpe Ratios and Portfolio Performance Evaluation I would go with the first paper.


10

The answer your are looking for might be the story in "Benchmarking Measures of Investment Performance with Perfect-Foresight and Bankrupt Asset Allocation Strategies", by Grauer (Journal of Portfolio Management). While this work main concerns are the differential ranking of various performance measures and with negative betas for market timing strategies, ...


7

In this case, the t-statistic is used to determine if the returns are statistically different from zero (the theoretical mean). A small t-statistic would imply that the null hypothesis (no significant excess return) cannot be rejected. Newey-West standard errors are used to correct for the correlations of error terms over time. I have written a Matlab ...


5

I would even stick to the original paper by Sharpe (1966): Mutual Fund Performance. The Journal of Business Vol. 39, No. 1, Part 2 pp.119--138 If you look at the numbers on Page 6 you can see that the funds sharpe ratios roughly are between $0$ and $1$. Since the Sharpe ratio already adjusts for the risk-free rate, you cannot really argue about its ...


5

Edited Comments: Sharpe Ratio covers both future and historical time frames (as @Freddy points out). Referencing the "Geometric Return and Portoflio Analysis", for the historical calculation, you want to make as few assumptions as possible (in my opinion). Let $m_i \triangleq$ the monthly return for period $i$ and $r_t \triangleq$ annual return, for $i\...


5

This optimization is trivial $$ w^{T,J}_i = \begin{cases} 1 \quad \text{if } i=\arg \max_i R^{T,J}(S_i) \\0 \quad \text{otherwise} \end{cases} $$ That is to say, when you optimize only one weight will be nonzero. That's because these ratios incorporate no notion of distributional width, and therefore do not reward diversification. With no concentration ...


5

For client reporting purposes, it is customary to use discrete returns. For backtesting, it pretty much make no difference.


5

Yes, you are correct on both terms - it doesn't make much sense, and there exists a well-cited solution by C. Israelsen: "A refinement to the Sharpe ratio and information ratio." Journal of Asset Management 5.6 (2005): 423-427. The adjustment he gives is to define $$SR_{adj} = \frac{r}{\sigma^{\frac{r}{abs(r)}}},$$ which solves the ranking problem during ...


4

Ideally you'd want to use daily returns and just annualise it, but if you only have monthly returns then calculating the weighted variance in the following way might do it: $$ Var = \frac{\sum_{i=0}^{24}(R_i - \mu)^2}{24 + \frac{21}{31}} + \frac{\frac{21}{31} (R_{25}' - \mu)^2}{24 + \frac{21}{31}} $$ $$ Vol = \sqrt{Var} $$ Where $R_i$ is the returns of ...


4

No, this is not the same. For example, consider the scenario $$ \begin{align*} r_A &= 10\% \quad\quad \sigma_A = 10\% \\ r_B &= 1.5\% \quad\quad \sigma_B = 1\% \\ \end{align*} $$ If $r_f=1\%$, $$ \text{SR}_A=0.90 \quad\quad \text{SR}_B=0.50 $$ then $A$ has the higher sharpe. Now if $r_f=0\%$, $$ \text{SR}_A=1.00 \quad\quad \text{SR}_B=1.50 $$ then $...


4

A short position is a liability on your books, as the borrowed asset has to be returned to the owner. The return is then the percentage return of that liability. Assume that the shorted asset at initial time $t_0$ has price $p(t_0)$. The initial liability is then $p(t_0)$. At a future time $t$ the liability is $p(t)$. The return at time $t$ is hence $$ r(t,...


4

Consider these two simple portfolios: Portfolio 1 returns -10% in month 1 and 10% in month 2. Average arithmetic return is zero, and cumulative return is $(1-10\%)(1+10\%)=0.99$. Portfolio 2 returns -50% in month 2 and 50% in month 2. Average arithmetic return is still zero, but cumulative return is $(1-50\%)(1+50\%)=0.75$, a much lower terminal value! In ...


4

Since you're looking to summarize the performance of a monthly return series in a single number, it is best to compute the annualized return. This is the standard used in the investment management industry. You could also compare your portfolio returns with that of an industry benchmark like S&P 500 on an annualized basis. Assuming your returns are in ...


4

I don't know that there is a "standard-solution crystalized in the community," but there are alternatives. The ones that I prefer are Omega, Sortino, and Kappa. All three of these ratios, unlike Sharpe, do not assume normally distributed returns. Omega Ratio: This is the probability-weighted ratio of gains versus losses for a given minimum acceptable ...


3

There is no universally accepted answer for the main problem here which is the denominator for the return calculation is zero or near zero. There are a few common solutions to this issue. The most simple solution is to use the total portfolio notional as the divisor for the PnL. This can be considered the PnL contribution of that long/short sub-portfolio ...


3

Martijn Cremers and Antti Petajisto have a series of papers using the concept of "Active Share," a new measure of active portfolio management which represents the share of portfolio holdings that differ from the benchmark index holdings, to evaluate mutual fund managers. They find that the most active stock pickers have outperformed their benchmark indices ...


3

I think you need to exactly define which ratio you are talking about. For example the ex-post Sharpe ratio's components are all well known. You have your realized returns, risk free returns (or whatever other benchmark you define your excess returns against) and realized volatility of returns. For realized asset returns you should not use log returns but ...


3

The PerformanceAnalytics library reflects several years worth of development by Brian Peterson and Peter Carl, as well as multiple collaborators. It is fairly widely used, tested and debugged. Basic software engineering practices suggest that you should strive to re-use it if possible. Options for that include accessing a remote R instance via RServe (...


3

Perhaps check out Poti and Levich (2009), or in a different setting but from one of the same authors, Poti and Wang (2010) "The coskewness puzzle" in JBF. They directly address the issue of what level of SR is plausible.


3

Pardon the lack of an actual link, and the formatting, but in footnote 6 of "Alpha is Volatility times IC times Score", Grinold, Richard C., Journal of Portfolio Management, Summer 1994 v20 n4 p9(8), Grinold suggests that "a truly outstanding manager" might have an information ratio of 1.33: (6) A rough guideline for determining the required IC comes from ...


3

In Quant Finance we start with the assumption that (until shown otherwise) no one can outperform a simple, passive benchmark. Such a benchmark might be for example the S&P 500 index leveraged up or down by borrowing/lending. To calculate your alpha we would obtain your monthly returns [actually excess returns $r-r_f$] for the past N months and regress ...


3

As @Alex C had pointed out, the CAPM and subsequently Jensen were probably the original motivations of the term $\alpha$. Bear in mind that $\alpha$ and $\beta$ are conventional notation for coefficients in a linear regression model, and quite easily as that, we can understand the intuition by thinking of this as an explanatory linear model of portfolio ...


3

For a single period return, the squared value of that return approximates variance (i.e., the absolute value approximates the standard deviation). Standard deviation is defined thus: $$\sigma_X = \sqrt\frac{\Sigma_1^N\mathbb{E}[X-\mu_x]^2}{N}$$ For a non-drifting process, $\mu_x = 0$. Also, in our scenario, $X = (r_a - r_m)$ and $N = 1$. Therefore, an ...


3

Both questions are not as straightforward as @Hui (and most academics and practitioners) would immediately think. I would try to put in my two cents to answering your question 1. Short answer: It might have to do with the bias-variance tradeoff, as measuring the alpha precisely is a tricky task in small samples (and young funds do have short histories). ...


3

I believe that by "luck" you mean that you want to check if you can attribute the pnl of your strategy to something else than the "alpha" that it's trying to capture. The standard way of doing this is by using standard market factors (such as Barra's standard risk model for equities say https://www.msci.com/www/research-paper/barra-s-risk-models/014972229 ) ...


2

This is a very common and serious problem among academic papers and with some hedge fund marketing material's, I can almost guarantee that the high ratio of 7 was with-out transaction cost's and that when included this 7 will drop down some where between 0 and 1.


2

cost of leverage for equity only long/short investing is a function of the margin deal you can negotiate with your broker, if you have a large amount of capital. If you don't have significant capital to start with, then it's likely you'll only be able to get 2x leverage with a loan rate between 4% and 10% (retail reg-t margin rates at most brokers) This ...


2

A very well thought through exposition on the matter is given in this paper: A Consultant’s Perspective on Distinguishing Alpha from Noise by John R. Minahan It combines a lot of wisdom and common sense that sometimes seems to get lost in the process...


2

My 2c worth. Experience tells me that the better ways to get a feel for whether their strategy is based on something more than luck are amongst: 1) `getting to know your traders' -- have a chat, pick their brains, try to get some insight into their methods; 2) see how hard the market has been -- check whether you have just been part of a bull market which ...


2

For analyzing a series of trades on a single stock over a period of time. You can understand your market timing contribution by comparing your actual return to the return from consistently holding your average exposure to the stock over that whole period. To then get a feeling for how much you are contributing compared to how much you are messing with a ...


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