What's new

# Value at Risk

#### FieryJam

##### New Member
Hi,
Just something fundamental that popped in my mind, I am thinking if value at risk ( Var) for a long portfolio composed of commodities assets will be higher in a high commodity price environment? Because 95th percentile vAR using delta normal approach will be 1.645*standard deviation* the value of the commodities portfolio. The commodities portfolio is equal to price of the commodity * commodity volume.
Do correct me if I am wrong.

#### QuantMan2318

##### Well-Known Member
Subscriber
Hi there @FieryJam
You may find this useful. It talks about the pro cyclical nature of VaR based on the approach employed based on the excellent discussions of @emilioalzamora1 and @David Harper CFA FRM

I would say that based on the number of observations (if you use Short Term observations, then the memory effect is amplified) that you use and the fact that Standard Deviation, which is a measure of volatility spikes in a crisis environment(like those of higher prices), the general trend is that in a higher price environment, VaR does tend to be higher

Thanks

#### ami44

##### Well-Known Member
Subscriber
Your calculation is correct, if by standard derivation you mean the standard derivation of the returns (also often called volatility).

If the standard derivation of the returns is constant your conjecture is true, that with increasing prices the VaR increases. If the standard derivation is e.g. 20%, independent of the price level, than the VaR increases with increasing price. Obviously 20% of a big number is more than 20% of a low number.

If the standard deviation is in fact constant depends on your underlying price dynamic. For a brownian motion, or a geometric brownian motion it's true. But other models exist (lookup CEV models if interested).
Of course the delta-normal method implicitly assumes a brownian motion for your risk factors i.e. the commodity price. But that is one of the weaknesses of the delta-normal method, we know that commodity prices are in reality seldom brownian motions.

In reality a positive correlation between prices and VaR exist as Quantman says in the previous message.

#### FieryJam

##### New Member
Your calculation is correct, if by standard derivation you mean the standard derivation of the returns (also often called volatility).

If the standard derivation of the returns is constant your conjecture is true, that with increasing prices the VaR increases. If the standard derivation is e.g. 20%, independent of the price level, than the VaR increases with increasing price. Obviously 20% of a big number is more than 20% of a low number.

If the standard deviation is in fact constant depends on your underlying price dynamic. For a brownian motion, or a geometric brownian motion it's true. But other models exist (lookup CEV models if interested).
Of course the delta-normal method implicitly assumes a brownian motion for your risk factors i.e. the commodity price. But that is one of the weaknesses of the delta-normal method, we know that commodity prices are in reality seldom brownian motions.

In reality a positive correlation between prices and VaR exist as Quantman says in the previous message.

#### FieryJam

##### New Member
Hi Quantman and ami44,
Fiery Jam

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@FieryJam it's a fascinating philosophical truth, I think, that you've identified. If I bought AAPL at ~ $70 (true story ) when it's VaR was 20%*α, now that the stock is over$150, has my dollar amount at risk doubled just because S*20%*α has doubled? I don't feel like it has! So many things to say about this, but here is just one thought: it could be a problem with standard deviation, right? Which notoriously is indifferent to the direction. I have not run a Sortino measure on AAPL's stock, but I bet you that the downside deviation is lower than the standard deviation (maybe my dollar downside deviation hasn't changed much even as the stock has doubled). In silly extremis, if an asset price mostly increases over a period, the Sortino could be nearly zero while the historical standard deviation is high. Put another way, we can imagine a growth scenario where a stock price doubles yet the downside deviation declines even as the standard deviation increases. So sometimes you get to a higher price and the percentage standard deviation, while mathematically fine, is not such a great input into a risk measure ... In any case, I agree with you too. Thanks!

Last edited:

#### Matthew Graves

##### Active Member
Subscriber
Just my 2 cents: It's important to remember that stock returns are heteroskedastic in general. When the stock price was \$70 AAPL was probably seen as riskier bet than now, hence higher volatility and higher VaR. The volatility has likely declined now that the price and stability of the returns has risen. Maybe an exponentially weighted volatility would be better when re-estimating your VaR?

#### FieryJam

##### New Member
Thank all for the replies. Interesting and thought provoking..

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Thank you @Matthew Graves (love that signature line "Certified FRM 2016")! My idea--to consider replacing standard deviation with downside deviation--was sort of narrow in comparison to Matthew's better, broader reaction: we have available the entire set of non-parametric alternatives and semi-parametric adjustments (adjustments to historical standard deviation, including age-weighting; e.g., we can measure VaR with volatility-weighted historical simulation which, in the current low VIX environment, would decrease the VaR as a function of lower current-regime volatility) that attempt to "remedy" the weakness of blindly calculating a standard deviation for some particular historical window. While Dowd is the primary FRM author on these topics, Carol Alexander's Volume IV is basically about many of the available choices (see https://www.bionicturtle.com/forum/resources/market-risk-analysis-value-at-risk-models-volume-iv.93/). Thanks!

Last edited:

#### kchalmers

##### New Member
Hi David,

I have a general question about when to include expected return and when not to include expected risk. As I understand it... absolute VaR does not include expected return whereas relative VaR does. Will the exam distinguish between the two?

#### emilioalzamora1

##### Well-Known Member
Hi @kchalmers,

It is the opposite way round:

1. Absolute VaR: - drift + (normal deviate * vol)

2. Relative VaR: (normal deviate * vol)

where drift = 0

https://www.bionicturtle.com/forum/...value-at-risk-var-dowd.3643/page-2#post-51392

No one knows what the exam will bring for exam takers but these two equations should not be too difficult to remember.

It depends: if you have a disproportionately large positive drift using the Absolute VaR notation then such a significant drift can somewhat bias the VaR figure (>>> make the VaR value smaller and therefore implying less risk).

In general this rule of thumb holds (should be applied) for daily return calculations: absolute VaR = relative VaR. In other words, daily returns should be assumed to be zero (at least if your sample is large).

Last edited:

#### kchalmers

##### New Member
Right sorry I mixed those up... thanks this is helpful!