9
votes
Accepted
Portfolio Risk Decomposition - different methodologies
Different portfolio risk decompositions answer different questions. Before discussing what method to use, first ask why you want a decomposition and what definition of risk are you using.
Is the ...
- 7,004
8
votes
Accepted
How are modern portfolio theory (MPT) and CAPM related?
CAPM states that the expected return of any given asset should equal $ER_i=R_f+β_i (R_m-R_f)$, with α being the error term of the previous equation. Now, as α has an expected value of zero, then only ...
- 516
7
votes
Accepted
What is the intuition of a spread portfolio and how exactly is it constructed?
Does variable $x$ forecast returns?
Let's say you have some variable $x$ that you think forecasts returns, and you want to conduct statistical tests of a null hypothesis that $x$ has nothing to do ...
- 7,004
6
votes
Accepted
Volatility of a multiple-asset portfolio
You can generalize the formula from a portfolio composed of 2 assets to a portfolio composed of $N$ assets as follows :
$$
\sigma^2_{port} = \sum_{i=1}^N \sum_{j=1}^N \omega_i \text{cov} (i,j)\...
- 1,219
6
votes
Accepted
Widely accepted methods for coming up with the co-variance matrix of assets?
Multivariate volatility models for replacing the sample covariance matrix with in the mean-variance portfolio selection model:
RiskMetrics 1996 EWMA (Exponentially weighted moving average) covariance ...
- 3,080
5
votes
Calculate Average Price, Cost, (Un)Realized P&L of a position based on executed trades
Using Andy Flury answer and bit polishing it gives following Python class for PnL calculator:
...
- 221
5
votes
Accepted
How to compute the variance of a Long-Short Equity Portfolio?
We have weights $w_A$, $w_B$ and $w_C = 1 - w_A - w_B$ that sum to $1$.
With de-meaned returns $r_A$, $r_B$, and $r_C$, the portfolio variance is
$$E\{[w_A r_A + w_B r_B + (1 - w_A - w_B)r_C]^2 \} = ...
- 3,700
5
votes
What is the delta of a portfolio invested in different stocks?
Strictly speaking, you cannot aggregate (i.e. sum)
deltas. However, equity traders often provide their net
exposure in currency units, which is a useful number. The same reasoning is
possible with ...
- 3,541
5
votes
Accepted
Sharpe Ratio and Sortino Question: Standard practice
Theoretically, Sharpe should be the average of (compounded) excess returns divided by the volatility of the same. It was designed to measure the risk-reward preferring the risk asset to riskless. So ...
- 5,101
5
votes
Why is a smaller portfolio norm better?
Norm constraints are motivated by regularisation in regression analysis. L1 and L2 norm are similar to Ridge and Lasso Regression. The author who first introduced this method argued that it will ...
- 988
5
votes
Best books on portfolio construction?
In addition to classical texts by Grinold and Kahn, and the sources cited in the previous answer, I can't help mentioning my book. It has a chapter on Portfolio Construction which includes alphas at ...
5
votes
Accepted
Information Coefficient (IC) Formulae Differences
Paraphrasing some quote:
"they are different but same but still different"
In reality the number of correct bets $N_c$ is the number of times the analyst was correct predicting the ...
- 886
5
votes
How to calculate the log return of portfolio?
Now this is a farily basic question, but since I see professionals having trouble with this all the time, let us go through it
Simple returns aggregate nicely (linearly) across trades but not time, ...
- 1,272
4
votes
Is there a way to meaningfully generate daily returns from monthly?
This is a commonly seen problem, and also relates to situations in which one is dealing with some less-liquid underlyings. I will describe a method that you could think of as "stochastic backfilling" ...
- 429
4
votes
how to calculate daily risk free rate using 13 week treasury bill
user233051 notes that ^IRX is indeed the official discount rate of the US Treasury. So to answer his question we need to exactly understand how the Treasury computes the discount rate. My answer is ...
- 140
4
votes
Variance Matrix with 'nan' values
This is a common problem in covariance matrix estimation, with several possible solutions. One of the simplest involves two steps:
(1) You compute each element of the covariance matrix on a 'best ...
- 11.6k
4
votes
Accepted
What is `1+ return` called?
It's called 'Gross return' (a.k.a. 'Gross Rate of Return'). See Zivot Course Notes Eqn. 1.8
Also, as pointed by Alex C:
... in Statistics it is called a 'link relative' or 'chain relative' (...
- 745
4
votes
What returns to use?
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 ...
- 61
4
votes
% Drawdown on Stock Portfolio to hit Margin Call
Define
CoL = cash or loan (cash if positive, loan if negative)
MVL = market value of long positions
MRP = Maintenance Margin Requirement fraction (=0.3)
NetLiq = liquidation value (aka total ...
- 9,402
4
votes
Accepted
How to calculate "portfolio cumulative return" from individual price data and weight of them?
These answers are missing the idea of path dependency. Your weights are only updated monthly. That means your weight on t0 is w0 and weight on t1 is w0*(1 + r1), weight on t2 is w0*(1+r1)*(1+r2) where ...
- 466
4
votes
What does risk tolerance represent for utility-maximizing optimization with linear constraints?
You cannot eliminate the dependence of a solution on the risk aversion parameter (which this author confusingly calls $\lambda$).
Perhaps a source of confusion?
Typically $\lambda$ is used to denote ...
- 7,004
4
votes
Calculating Correlation of Two portfolios?
You may be over-thinking it. It is a straightforward calculation using matrices, as easy as turning the crank of a sausage-making machine.
The standard deviation matrix is
...
- 9,402
4
votes
Accepted
Why annualizing sampled covariance matrix changes stock weight vector?
Q1. Calculating the GMVP involves three operations:
Inverting the covariance matrix $\Sigma$
Multiplying the inverse by a column vector of 1's on the right: $x=\Sigma^{-1} \mathbf{1}$
Normalizing ...
- 9,402
4
votes
Accepted
Active portfolio management - characteristic portfolios derivation
Below proposition 1 (In the 2nd edition at p. 28?), at the beginning of the chapter, he specifically writes:
Characteristic portfolios are not necessarily fully invested. They can include long and ...
- 4,726
4
votes
Accepted
Show that the following result holds true for the variance of the return of a portfolio of shares
The variance part is correct.
For the covariance part we can observe the following: There are $n$ variance terms in the $n \times n$ covariance matrix. This implies that there must be $n^2-n$ ...
- 4,726
4
votes
Accepted
Best books on portfolio construction?
I can list a couple of things that are very reasonable to start off with. As written in the above comment, you will not be able to find any "secret sauce" in books and journals. You will, ...
- 4,726
4
votes
How to set a fixed return for mean-CVaR portfolio optimization?
I don't use fPortfolio but when I run your code example, I first get an error:
...
- 3,541
4
votes
Accepted
Literature about optimal number of stocks in a diversified portfolio
The first article on this was Fisher and Lorie "Some studies of variability of returns on investments in common stocks" JB April 1970.
https://www.jstor.org/stable/2352105
The Statman ...
- 11.6k
4
votes
Can I invest in the market portfolio of modern portfolio theory?
This "market portfolio" is a chimera: very useful for basic reasoning and teaching, but that cannot be traded. Here are three reasons why
the term "market" suggests that it is ...
- 12.5k
4
votes
Accepted
Log return on short selling when the loss exceeds 100%
The easiest way is to think for a return on a short position as being the negative of the return on the long position. In that way you never get confused.
Think about the following example. On day 1 ...
- 8,561
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