# Tag Info

6

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 ...

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

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 ...

5

You are right to be sceptical of the beta of an international portfolio when it is calculated using daily returns. Beta estimates are often low for international portfolios because stock market returns are asynchronous. For example, Tokyo and the New York Stock Exchange have very different trading hours. Portfolios constructed with a tilt towards either ...

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 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 ... 4 Thanks for the example. It is exactly like my comment. Look at your weights after the first period. Are they really 80% and 20%? Lets say you have £100 to invest. £80 is invested in product A. That turns into £81 after the first period and £79.38 (81*(1-0.02)) after the second period. Total return is 79.38/80 = -0.775 \% £20 is invested in product B -&... 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 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 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 More measurable effects to add to your list: "window dressing" - returns of the fourth quarter or 12th month (i.e. year-end) are higher on average than oher returns; the same to returns of 4th months (qtr-end) vs. others; "herding": changes in asset-classes shares of "big" funds (whatever you define "big") granger-cause changes in asset-classes shares of "... 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 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 ... 2 Firstly, I suggest you to use more recognized source to study and compute quantitative finance model or indicators; in such case, for instance, you could take as example the following paper as reference. Precisely there, the authors describe some common errors that one can do in computing the Sortino ratio; although surely you did not do any of them, ... 2 In theory, stock prices are lognormally distributed. People usually prove lognormality by referring to positivity and right skewness of stock prices. Mathematically (or philosophically if you wish), lognormality follows from the following equation$\frac{S}{dS}={\mu}dt+{\sigma}dW$, which you may see a lot in quantitative finance ("random walk") or in ... 2 I think the only valid answer is you can't. The techniques you describe would work of the signal was much stronger than the noise but it seems that with your fund returns this is not the case. You could try to get more data or look at other risk measures like max drawdown to get some idea of the risks involved. 2 The best way to check the accuracy of a Garch model is to use the methodology of Hansen and Lunde (2005). In this paper they actually compared the accuracy of 330 Arch-type models and concluded that Garch(1,1) was superior in their sample. The paper describes at great length the way to do it. But in a nutshell: Estimate arch-type your model in monthly ... 2 Adding to Attack68 answer- you can do a few things: calculate total and average pnl over a given time. calculate skew, kurtosis etc. as suggested above. calculate hit rate. calculate max drawdown. SR using daily pnl is fine but ideally the returns should be in %. 2 It depends on the ratio you are looking at. Most of them are scaled by$\sqrt{12}$, but the Treynor index is a bit different and is scaled by$12\$. Sharpe and Information ratios are both ratios of average returns to standard deviations. They are annualized by assuming that the monthly returns are IID. Hence, average monthly return is scaled up by 12 and ...

2

Check out empyrical. This library provides methods for calculating several risk and performance metrics. pyfolio is also a great tool for visualizing your portfolio's performance over time.

2

Max drawdown of a portfolio is the loss relative to a previous high-water mark. It's typically calculated as you describe, calculating cumulative performance and maxDD relative to the previous equity peak. I'm not aware of a built-in Matlab function (speaking as someone that built a backtesting suite in Matlab years back, including max DD by hand), so ...

2

Depending on your version: Matlab 2019 https://www.mathworks.com/help/finance/maxdrawdown.html Matlab 2018 or before https://in.mathworks.com/matlabcentral/fileexchange/10367-maximum-drawdown The latter is a user-defined function and not a built-in by MathWorks. The developer is Andreas Steiner.

Only top voted, non community-wiki answers of a minimum length are eligible