17
votes
Accepted
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 $...
- 15.1k
10
votes
Accepted
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 ...
- 1,307
10
votes
Accepted
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:
$r = log(R+1)$
- 4,728
10
votes
Accepted
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 ...
- 5,001
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 ...
- 7,827
8
votes
Accepted
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 ...
- 717
8
votes
Accepted
6
votes
Accepted
Calculating log-returns across multiple securities and time
In Python, simple geometric returns:
...
- 741
6
votes
Accepted
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 ...
- 27.3k
6
votes
Accepted
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 ...
- 932
6
votes
Accepted
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 ...
- 2,876
6
votes
Accepted
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 ...
- 8,436
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 ...
- 1,082
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 ...
- 7,669
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 ...
- 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:
...
- 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 ...
- 111
5
votes
Accepted
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.
- 11.3k
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 ...
- 5,949
5
votes
Accepted
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 ...
- 4,299
5
votes
Accepted
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 -...
- 11.3k
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 ...
- 11.3k
5
votes
Accepted
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\...
- 6,174
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 (...
- 15.1k
5
votes
Accepted
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.
- 750
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 ...
- 7,827
5
votes
Accepted
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 ...
- 6,864
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.
- 8,436
4
votes
Computing Pooled IRR from the IRRs of parts
No there is no way since the calculated internal
rate of return $r$ is by definition defined as:
$0 = \sum_{i=0}^{I} \frac{C_{i}}{(1+r)^{i}} $
You need to know the entire cash flow distribution ...
- 2,542
4
votes
Computing Pooled IRR from the IRRs of parts
Exact solution:
Assume we agree that for
$y_1:=IRR(CF1)$, $y_2:=IRR(CF2)$, $y:=IRR(CF1+CF2)$, the following equations hold by definition:
$$-1000+\frac{100}{1+y_1}+\frac{100}{(1+y_1)^2}+\frac{1100}{...
- 5,739
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