19
votes
Quantifying climate change risk
Here are some resources that I found useful when learning about this subject, in which I'm very interested. (Some may be more general ESG than just just climate.)
Citigroup. Environmental and Social ...
- 12.6k
10
votes
Accepted
Intuitive explanation for expectiles
No reply has been given so I wanted to at least give a visualisation of the expectiles.
Suppose the curvy dashed line in my picture represents a cumulative distribution function of some random ...
- 1,527
10
votes
Accepted
Kelly criterion for normally distributed returns
This problem can be expressed as the original Merton's portfolio problem.
Consider wealth process defined by SDE
$$
d X _ { t } = \frac { X _ { t } \alpha _ { t } } { S _ { t } } d S _ { t } + \frac ...
- 427
10
votes
Which is riskier: a call option or the underlying?
A better, clearer, answer is to compute Lambda (leverage) of the option (link) and see if it is bigger or smaller than 1. Lambda is $\Delta \frac{S}{V}$ so we test
$$\Delta \frac{S}{V} \lessgtr 1$$
...
- 11.6k
9
votes
non-subadditivity of VaR
Simple example where sub-additivity fails
Let there be four possible outcomes $i=1,2,3,4$ that occur with equal probability $\frac{1}{4}$. Payoffs for $X$, $Y$, and $X + Y$ are given by:
$$ X = \...
- 6,994
8
votes
Accepted
Which is riskier: a call option or the underlying?
As @ir7 did, I only briefly want to add to @noob2's spot-on answer. He's of course right and $\Lambda=\Delta\frac{S}{V}$ decides how risky the option is compared to the stock.
Firstly, note that $\...
- 16.2k
7
votes
Accepted
How to check if a portfolio has momentum bias
It kind of depends what your objective is. First, momentum 'bias' isn't well-defined. Are you looking to eliminate momentum exposure for some reason? Momentum itself isn't even well-defined really: ...
- 1,651
6
votes
What is the best alternative of Quantlib library
I did not tested it by now, but Google released a library similar to quantlib written in TensorFlow (tf-quant-finance). It may be worthwhile to test it (and to post here your views on it), because ...
- 12.5k
6
votes
Accepted
non-subadditivity of VaR
VaR is not sub-additive in general.
Relying on Mark Joshi comment, there are particular cases where it can be. Such cases occur for portfolios containing elliptically distributed risk factors. Of ...
- 1,219
6
votes
Accepted
What is an accepted method to calculate percent PnL from a short position?
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 ...
- 1,034
6
votes
Accepted
Construct a butterfly interest rate portfolio to eliminate PCA exposures
Let $S$ be your risk sarray, expressed in pv01, for each of your (implied) 10 instruments. You restrict the array to all zeroes except those corresponding to the 5Y, 7Y and 10Y risks, e.g. if 1Y:10Y ...
- 11.2k
6
votes
Accepted
Book recommendation
First, a word of caution
One of the problem with mathematical finance, as well as the related field of financial economics is that there is more than enough to learn to fill your schedule several ...
- 2,506
6
votes
Accepted
Variance attribution calculation from a covariance matrix
Suppose the covariance matrix is $V$ (which is n by n) and the weights are $w$ (of length n).
Then the Portfolio Variance is $V_p = w^T V w$
and the Risk Contribution (in terms of variance) of asset ...
- 11.6k
6
votes
Which is riskier: a call option or the underlying?
Just a small addendum to @noob2's answer. The discrete shape of $\lambda$ is:
$$\lambda \approx \frac{V_1 - V_0}{S_1 - S_0} \times \frac{S_0}{V_0} $$
which can be rewritten as
$$ \lambda \approx \frac{...
- 5,113
5
votes
Accepted
Overestimating or underestimating risk?
Yes, it is correct.
Underestimation: you under-estimate the risk, so you have more VaR violations than what your model predicts. Ex: With 100 observations, and a 99% VaR, you expect 1 violation but ...
- 2,582
5
votes
How to construct a Risk-Parity portfolio?
Another approach to construct a risk parity portfolio would be to use the formulation proposed by Spinu [1]: $$\begin{array}{ll}
\underset{\mathbf{w}}{\textsf{minimize}} & \frac{1}{2}\mathbf{w}^{T}...
- 106
5
votes
Accepted
Question on Rockafellar's Paper for optimisation of CVaR
On 1, I suspect that is a typo and that the second formula should sum to r.
On 2, that is applying well-known techniques in how to handle piece-wise linear functions in an optimizer. For instance, ...
- 5,421
5
votes
Accepted
Can portfolio Value-at-Risk be calculated analytically for multivariate t-distributed returns?
Let the $n-$dimensional vector of returns $\mathbf{r}$ have a multivariate t distribution with $\nu$ degrees of freedom. The marginal distribution of any component $r_i$ has a univariate t ...
- 3,700
4
votes
ES not elicitable
I think it was T. Gneiting in 2011 who first proved that ES is not elicitable (Making and Evaluating Point Forecasts, Journal of the American Statistical Association Volume 106, 2011 - Issue 494) , ...
- 429
4
votes
Accepted
A comprehensive list of risk measures for different asset classes
VaR has the benefit that it is comparable across all asset classes, and can even be computed for multi-asset class portfolios. The downsides are that it either needs assumptions on the joint ...
- 5,931
4
votes
Accepted
What instruments help me receive a premium?
no, generally speaking only options has time premium. I strongly advise you to avoid mixing 2 positions (short 1 option, long another one) in your mind just because they are independent, so just ...
4
votes
Accepted
Types of risk for stock investing
Just wanted to check that there is not any FX risk here, as the US
investor has bought $ donimated stock, so it is irrelevant that Toyota
is also traded in Japanese markets in Yen.
An American ...
- 4,358
4
votes
Hierarchical Risk Parity with allocation constraints?
EDITED
You are right. We have to look town to the "leaves" in each iteration. I would do it the following way:
If $L_i^{(j)}$ is the set of indices in the $j$ branch ($j \in \{1,2\}$), then we ...
- 2,935
4
votes
Intuitive explanation for expectiles
That picture in the other answer is pretty slick (+1), so I will just add a note on why one can interpret the colors of those areas like that:
Blue:
Define $Y = (X-x)_+$. This is nonnegative r.v., ...
- 554
4
votes
Accepted
Does longer time horizon necessarily imply reduced risk?
It depends upon how you define risk.
Assume a constant, positive equity risk premium and an equity index following geometric Brownian motion (GBM):
$$d \log S_t = \mu \, dt + \sigma \, dZ_t = (\hat{\...
- 3,700
4
votes
Accepted
Structured product sellers and div swaps
The paper is generally correct, but it is not a general statement, as in a general truth of options hedging in a theoretical context, rather a statement regarding how the structured derivs market is ...
- 1,406
4
votes
Structured product sellers and div swaps
To add to the above on a more practical note:
In general, SP desks make money on the individual product when the underlying declines. Dividends make the underlying decline, hence they are naturally ...
- 161
4
votes
Accepted
Semivariance calculation (downside deviation)
I am interested in Semivariance because I want to use it to compute the Sortino Ratio. I found an article on Sortino which answers to my question. Here is the link "Sortino ratio: A better measure of ...
- 296
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