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17 votes
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Term structure of Equity returns

Intro: Duration-Based Asset Pricing Similar to bonds, we can define the duration of stock $i$ as $$ Dur_{i,t} = \sum_{s=1}^\infty s\cdot\frac{\mathbb{E}_t[CF_{i,t+s}]e^{-s r_{i,t}}}{P_{i,t}},$$ where $...
Kevin's user avatar
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11 votes
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Returns and logreturns differences

OK, this need have nothing to do with any single sample of data. It's an inherent difference between the behaviour of linear vs logarithmic numbers. Which is what make up your respective simple and ...
demully's user avatar
  • 5,071
10 votes
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Reasons for negative autocorrelation

Looking at transaction prices, they would occur at the market bid if the active part is a seller, and at the ask if the active part is a buyer. With a random flow of sellers and buyers, the price will ...
Mats Lind's user avatar
  • 1,412
10 votes
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Convert arithmetic returns to log returns

Transmuting one to the other is pretty straightforward without the underlying sequence of prices. To go from log to simple: $R = exp(r) - 1$ To go from simple to log: $r = log(R+1)$
amdopt's user avatar
  • 4,348
9 votes

What is the difference between squared returns and variance?

Usually the formula for the sample variance of a stock is given by: \begin{equation} Var(R_{i}) = E (R_t - E(R_t))^2 \end{equation} If you are using daily data to compute the variance then the ...
phdstudent's user avatar
  • 8,381
8 votes
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How can I measure returns such that the average is useful?

Take the log return between days.
Newquant's user avatar
  • 769
7 votes
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Risk-adjusted returns ratio that does not reward high risk for negative returns

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 ...
Forgottenscience's user avatar
6 votes
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Calculating the returns of a long/short strategy

There are two ways to calculate the returns. One way is to calculate the net asset value (NAV) of your portfolio. For the long side the NAV is the value of your stock holdings. For the short side the ...
RRG's user avatar
  • 1,024
6 votes
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Predict probability of returns: How does changing volatility affect the return pdf?

I have written an entire paper on this approach at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2828744 As to your specifics 1) "Volatility" as defined by variance does not exist, which is ...
Dave Harris's user avatar
  • 4,299
6 votes
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If markets are efficient, why are most returns systematically high?

What you describe is known as the Equity Premium Puzzle - and it really is, as the name says, a real enigma: "The equity premium puzzle (EPP) is a phenomenon that describes the anomalously higher ...
vonjd's user avatar
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6 votes
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When modelling ARCH/GARCH effects, do we use excess returns?

GARCH models have little to do with the economics of the data generating process of the series you model, so both returns and excess returns (and log-returns, and inflation-adjusted ones, even ones ...
Igor Pozdeev's user avatar
6 votes
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CAPM - Expected vs. actual returns

Based on your comments on other answers, i would like to provide you a summary on the difference of the CAPM-Alpha and Jensen's-Alpha. CAPM The CAPM is an economic model for asset pricing. It states ...
skoestlmeier's user avatar
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6 votes
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Is it always better to use the entire distribution of a financial returns series, not just $\mu$ and $\sigma$?

It depends. For example, if you're doing option pricing in the log normal world returns are completely described by the mean and standard deviation. If you add jumps, you would also need to ...
Bob Jansen's user avatar
  • 8,562
6 votes

Are cumulative returns stationary?

Hi: Even if returns were stationary ( which is probably dependent on the time series one is considering ), cumulative returns, where $n$ is not fixed ( as it in say a rolling sum with a fixed window ...
mark leeds's user avatar
  • 1,112
6 votes

How can I measure returns such that the average is useful?

What does not work with the geometric mean? The geometric mean is computed with the following formula: $${\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots ...
AKdemy's user avatar
  • 8,934
5 votes

Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?

The correct answer is "arithmetic mean, because Bill Sharpe says so". He invented the thing, and he's pretty clear on which one he was looking at. If you use the geometric mean, which is lower the ...
m.a.i.'s user avatar
  • 51
5 votes

Calculate Average Price, Cost, (Un)Realized P&L of a position based on executed trades

Using Andy Flury answer and bit polishing it gives following Python class for PnL calculator: ...
mde's user avatar
  • 221
5 votes

Fama-French Data from daily to monthly returns

You're compounding correctly but the discrepancy is not just because of rounding. SMB and HML are formed as averages of 6 and 4 different portfolios, respectively. As French's website explains, this ...
Cyurmt's user avatar
  • 111
5 votes
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Sharpe ratio: discrete or continuous returns?

For client reporting purposes, it is customary to use discrete returns. For backtesting, it pretty much make no difference.
Helin's user avatar
  • 11.7k
5 votes

Proof that linear returns aggregate across securities

I think you are simply confusing percentage weights and number of assets. In your definition the initial percentage weight of the $m$ assets in the portfolio are given by $w_i^{t - 1}$ and they sum ...
LocalVolatility's user avatar
5 votes
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average return Vs cumulative return interpretation

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 -...
Helin's user avatar
  • 11.7k
5 votes

Have any other factor "styles" which explain equity returns been uncovered?

A wonderful recent paper that might be of interest is Feng, Giglio, and Xiu's "Taming the Factor Zoo." First, the paper lists nearly 100 "factors" that have been proposed from 1965 through 2016. The ...
Helin's user avatar
  • 11.7k
5 votes
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How to calculate necessary gain to compensate a loss in a financial transaction?

Let x represent the percent change-e.g. 2%, let k represent the number of decreases, and z the number of increases. Something like this? We want to find z such that: $\left(1-x\right)^k\left(1+x\...
Magic is in the chain's user avatar
5 votes
Accepted

Normality or Log-Normality of Regular Returns

You're right but a GBM doesn't assume that percentage returns are normally distributed. It's about log-returns. If the log-return $r_t=\ln\left(\frac{S_{t+dt}}{S_t}\right)$ is normally distributed (...
Kevin's user avatar
  • 16k
5 votes
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Calculating Dollar-Neutral Strategy Net Return

Yes, you can just do IGE - SPY if you assume the short finances the long. The Sharpe ratio will be the same whether or not you divide by 2.
Quantoisseur's user avatar
5 votes

Term structure of Equity returns

The term structure of returns refers to returns on assets with the same underlying cash flows, where the return is measured over the same holding period, but for different maturities. The price of a ...
phdstudent's user avatar
  • 8,381
5 votes
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Are Fama-French returns in percentages?

In my experience working with Ken French's data library, a "1.37" in the return field would correspond to a 1.37% return (with rounding to the hundredths place). You can of course do some ...
Matthew Gunn's user avatar
  • 6,954
5 votes

Am I able to find individual returns from total weighted average of returns?

You have one equation and three unknowns, as you found out this can’t work. You need at least as many independent equations as unknowns. I don’t see how you can make this idea work.
Bob Jansen's user avatar
  • 8,562
4 votes

Calculate weekly returns from daily stock prices?

Your second formula regarding the sum of day-to-day returns collapses as follows: $$ \begin{align} R_{weekly,2} &= \text{log}(Price_{Mon}) - \text{log}(Price_{Sun}) \\ &+ \text{log}(Price_{...
Richard Hardy's user avatar
4 votes
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Control for non-synchronous trading in correlations

I contacted one the authors of the original paper. He confirmed that the overlapping three day log returns are to be used on both stock and market returns.
Mike Haye's user avatar
  • 193

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