# Value at Risk for Portfolio of Futures

I'm working in a very small commodity trading company. They are not used to excel at all, so i built their trading sheet to follow open positions & past positions.

Now they asked me to calculate the VaR of the total portfolio.

I have never done that, so I read a lot of ressources on the internet, especially topics on here, but none of them really explain on how to do it precisely. I'm calculating historical VaR

The portfolio is made of futures & options

They dont roll the futures. They keep the positions for a relatively short time (2-3 weeks)

We have deposited 20k$at the bank So I tried doing it: I choose the number of windows (1 year) so 250 cases I collected historical return of futures on t-1 I applied that return on t-1 to today futures position and record dollar P&L This is my first question. What does it mean to today's futures position ? I saw someone on youtube multiply it by the value of my portfolio (20k$) ?

I repeat but change t-1 to t-2 and so on until I have 250 cases I then choose my significance level (5%) I rank those 250 P&L and get 5%th lowest percentile (top 5% most negative P&L)

But the result is only for one futures position, how do i add different VaR to have the total VaR of the porfolio ?

Because i have futures & options, and I don't know how to calculate the weight of each positions. Some people say to use the initial margin that i keep at the broker, but i wanted to be sure.

• For a portfolio of Futures and Options I usually compute the VaR as a dollar amount not a percentage return precisely because it is unclear what the return on a future is. If people want to know the percent I divide by the Liquidation Value of the portfolio. But most peole prefer the dolar amount. However you could also divide the dollar VaR by the initial margin requirement on the portfolio as your colleague suggested; I don't disagree with that choice. Oct 20, 2023 at 19:17
• The initial margin was an idea suggested on here hahaha. But i will keep it as a dollar amount as you and the other comment have suggested. So my method is mostly correct, i just need to multiply it by the notional value to get a dollar amount right ? Thank you for your answer
– Koba
Oct 23, 2023 at 8:19
• Yes, so yesterday the price of December ES contracts (S&P Eminis) was 4248.50. The dollars per point is 50, so the notional value of 1 contract was 212,425.00 usd. If 2 contracts, then twice this, etc. If today the price goes up 10, then the NV increases by and you will have made 10*50 = 500 usd per contract. OTOH for Crude one ctct is 1000 barrels, so on 1 ctct you make/lose 1000 usd per point of price change. The dollars per point for each contract is the key parameter (for finding both NV and P&L) and can be easily found on the exchange web site. HTH. Oct 23, 2023 at 12:37
• Thank you a lot !!! I'm trading sugar 5 & sugar 11 contracts, the NV of contract 11 is 29 825.6. And for a contract 5 is 36 085 today. With a multiplier of 1120 for sugar 11 & 50 for sugar 5 Im gonna apply what you said to my calculations ! One last question. Do you do your VaR calculations on a daily basis ? Or everytime that there is a change in your portfolio (new entry or sale of futures)?
– Koba
Oct 23, 2023 at 13:30

Futures and options are financial derivatives, and one key feature is their inherent leverage, which means you don't need to have the full cash equivalent to finance the market risk they represent. You'll need to know the contract size of each instrument so as to get their notional value.

In the context of historical VaR calculations, estimating correlations is not a concern. You can calculate VaR for each position by using the time series of returns and the notional value of each position. Then, add up these results to determine the portfolio VaR in dollar value.

As mentioned earlier, expressing VaR in percentage terms doesn't provide meaningful insights for a portfolio of derivatives.

• So i'm trading contract 5 & contract 11 of sugar. So the notional value today of for a contract 11 is 29 825.6. And for a contract 5 is 36 085 today So I need to multiply my daily returns of each contract to the notional value for each contract ? Thank you for your detailled answer.
– Koba
Oct 23, 2023 at 8:18
• What you need is the notional value in dollars. Is that the case for the figures you provided? Once you have then, multiply it by the returns in your time series, then look for the 95 percentile. Oct 23, 2023 at 12:14
• Yes its a dollar amount, thank you very much ! One last quesiton, do you do your VaR calculations on a daily basis ? Or everytime that there is a change in your portfolio (new entry or sale of futures)?
– Koba
Oct 23, 2023 at 13:33
• If the relevant market prices change, your VaR estimate will also change, even if the portfolio hasn't been changed. It really depends on how critical the position is at your firm. For financial institutions in general, VaR is usually estimated daily. Oct 23, 2023 at 15:34
• Thanks a lot !! Im gonna try to automate the process in Excel
– Koba
Oct 25, 2023 at 8:25