# Tag Info

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Scaling volatility as you do is often leading to inaccurate results which is over-estimating volatility especially when you scale daily volatility to even longer periods. Please see the following for more: http://economics.sas.upenn.edu/~fdiebold/papers/paper18/dsi.pdf The above paper also explains why scaling the way you did does not properly account for ...

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I think you may be interested in this QJE forthcoming article by Ian Martin. The key idea of the article (page 5) is that the expected return on the market can be decomposed as $E_t[R_{t+1}]-R_f = \frac{1}{R_f}Var^Q(R_{t+1}) + \text{extra terms}$ As you correctly pointed out the expected return should be related with the risk neutral variance. The issue ...

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The question you ask is in fact about what people in machine learning call overfitting: the more you choose your "metaparameters" to provide high returns on your sample of days the less you can trust them to reproduce out of this sample. There is not a lot you can do to prevent this except read a lot to understand overfitting and be very careful. Two main ...

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for the square-root rule: it holds for log-returns, if you assume the same variance and no autocorrelation. Because then: $$Var[r_1 + \cdots + r_d] = Var[r_1] + \cdots + Var[r_d] = d Var[r_1]$$ and thus $$\sqrt{Var[r_1 + \cdots + r_d] } = \sqrt{d} \sqrt{Var[r_1]}.$$ This is mathematically true for any distribution that fulfills the assumptions. For the ...

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No, it would be $$(RI_{t}-RI_{t-1})/RI_{t-1}$$

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You have the parentheses in the wrong place! The correct formula is $$\sigma^2 = \frac{1}{n-1}\left(\sum_{i=1}^n\ln^2\left(\frac{C_i}{C_{i-1}}\right)\right)-\frac{1}{n(n-1)}\ln^2\left(\frac{C_n}{C_{0}}\right)$$ To see this, start with your original formula and expand. \begin{align} \sigma^2 &= \frac{1}{n-1}\sum\left[\ln\left(\frac{C_i}{C_{i-1}}\... 3 I'm guessing {W_t^r} and {W_t} correspond to real and nominal endowment at time t, respectively, and that {P_t^g} is the price level at time t. In that case, W_t^r \equiv W_t/P_t^g follows, and if endowment grows at a nominal interest rate R_t, then W_t = W_{t-1}(1+R_t). We can write W_{t-1}=(W_{t-1}^rP_{t-1}^g), so by substitution W_t=(W_{... 3 It looks like 1 and 2 are different portfolios of companies. 1 is a portfolio of dual-listed companies, and 2 is a portfolio of everything in the "market". Once you have constructed these these portfolios, let's say you put the returns for every time step into a vector, call it r, then the average return would be mean(r). You need some clarification as ... 3 When volatility is high, daily volume is high. And when volatility is high, daily returns are high. That's why when volume is high, the price returns are high. Volatility (like volumes) is autocorrelated. This is the phenomenon of volatility clustering (large changes tend to be followed by large changes, of either sign) and volume clustering (large volumes ... 2 The basic CAPM - which is what your regression estimates - says R_S = R_f + \beta_S (R_{Market}-R_f) $$where$$ \beta_S = \frac{Cov(R_M,R_S)}{Var(R_M)} $$i.e. the return of a certain stock depends only on the correlation with the market portfolio. For your pricing equation to work, you will need to have an idea about the expected market (excess) ... 2 No, the "low-beta" anomaly is not the result of the difference between arithmetic and geometric mean returns. Statistical tests verifying the existence of the anomaly rely on models employing the arithmetic mean returns,$$\mu_a = \mu_g + \frac{\sigma^2}{2}$$, hence the penalty excess volatility incurs when compounding returns over time does not explain the ... 2 The technical analysis point of view: an increase in volume (assuming the price has been in a downtrend) means the crowd are throwing in the towel, i.e. everyone is dumping the stock and assuming that hoped-for rise is now never going to happen. The same on the way up: everyone jumps on the bandwagon. In other words, high volume typically means crowd ... 2 They are both excess returns even though the standard convention is to talk about risk premium for R_{t+1}-R^f and excess return on the market for R_{t+1}-R_M. If you believe in CAPM, then you need the former to compute:$$\alpha= (\bar{R}-R_f) - \beta(\bar{R}_M-R_f)$$By definition, the excess return is the payoff of a portfolio with price zero today, ... 2 Actually prices dont make sense as they are correlated with previous samples (prices), returns are not. Better will be difference between prices, but then you dont have reference point and comparability between assets, so eventually you need returns. At the end that is what you are interested in I think as profit is usually measured in return. 2 I think the only valid answer is you can't. The techniques you describe would work of the signal was much stronger than the noise but it seems that with your fund returns this is not the case. You could try to get more data or look at other risk measures like max drawdown to get some idea of the risks involved. 2 Sure! Sharpe ratio must be defined as the return per unit risk on a zero-cost position. The notion you are referring to achieves this by assuming borrowing at a risk-free rate before investing, so refinancing risks should matter. On a side note, the Sharpe ratio of any ForEx strategy would implicitly have the stuff you mention accounted for. 2 You do not have to think too much about return formulas and get confused, just go to the basics. Return is simply:$$ Return = Ending Value / StartingValue - 1  Log returns are used in places where it provides model simplicity in defining returns in a logarithmic format. Also when assumptions are made on log-normality rather than normality. Log returns ...

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The key word in your question is compounded. The expected arithmetic return for each $\Delta t$ is $\mu$, but the growth rate is $\mu - \frac{\sigma^2}{2}$. As others mentioned, volatility reduces the growth rate. This is similar to the area of a rectangle. If one rectangle has sides 3 and 1, its average side length is 2, and its area is 3. If another ...

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I would recommend you to convert your global portfolio returns into US-$Kenneth French provides several global factor-returns for the entire global stock market of developed countries. The description states, that all returns are in U.S. dollars, include dividends and capital gains, and are not continuously compounded. Further: [...] The global ... 1 Your approach is right: Take all the cash flows (outgoing with negative signs and incoming with positive sign), for unrealised take the NAV. If you don’t have NAV, then you will need to find a way to estimate the net value of the underlying portfolio, and the estimation approach would depend on the nature of the assets in the portfolio. If you know nothing ... 1 The issue comes from below two variables are defined outside of do...while... var resultValue = 0; var irrResultDeriv = 0; These statements need to be moved to immediately after the "do {" as they provide initialization for the two "for" statements immediately following. 1 I think there are 2 approaches being a bit mixed up here. You can analyze the option market by looking at implied volatilities and apply Black-Scholes (BS), thus assuming that log-returns follow a Gaussian distribution. Implied volatilies are the parameters that bring together BS and market prices. Then you will observe a pattern of implied volatilies for ... 1 What is the mapping between log return$r_l$and arithmetic return$R_A$? It is$r_l=\ln(1+R_A)$and$R_A=e^{r_l}-1$. If$r_l$has the normal distribution then$e^{r_l}$has the lognormal distribution (by definition) and$e^{r_l}-1=R_A$has the "lognormal distribution shifted to the left by 1". I don't think there is a name for this distribution, which has ... 1 Although this question is not a good fit for this forum (too basic) I answer it anyway: It means that both are statistically independent. So intuitively when one income stream goes up the other either goes up too, or goes down or stays the same - completely independently. 1 To get one-month rate X from three-month rate Y, you use this formula: 1 + X = (1 + Y)^(1/3) To get one-month rate X from annual (12-month) rate Y, you use this formula: 1 + X = (1 + Y)^(1/12) To get three-month rate X from annual (12 month) rate Y, you use: 1 + X = (1 + Y)^(3/12) 0.25% is annual 3% converted to a monthly rate, i.e. (1+0.03)^(1/12) - 1 ... 1 I'm currently also using daily returns which I want to annualize. This is my approach: For every month, I calculate the simple return using the formula: (end-of-month closing price / beginning-of-month closing price) - 1. I use the Excel formula somproduct(geomean(A1:A12+1)-1) to find the monthly compounded return. Finally, I annualize the result of step 2 ... 1 It depends on your investment strategy. The most common approach is to use the close price of$p_t$and$p_{t+1}\$. The volatility you measure using this method implies the "assumption" that your are able to trade at close every day. If you choose to compute the daily returns from open to close, then you assume that you are selling your position every night ...

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