Calculating VAR for large, levered positions | September 20, 2006
by Byron Binkley
When I read the "What Went Wrong at Amaranth?" article today, it made me wonder whether you have to be a convertible-bond trader making natural gas bets to get in trouble with paper gains, leveraged investments, and liquidity. The WSJ wrote,
Amaranth's systems didn't appear to measure correctly how much risk it faced and what steps would limit losses effectively… They also might not predict how much selling of one's stakes to get out of a position can cause prices to fall.
Couldn’t this problem face any hedge fund putting increasing amounts of capital into play with traditional equity strategies? If you have a $20 million in a micro-cap position, does your risk report take liquidity into account for VAR calculations? Perhaps more concerning is the implied liquidity concerns for lenders who don’t have transparency into the full book or depth of positions with funds that keep positions with multiple prime brokers.
Out of curiosity, I wanted to look at VAR with very basic, user-adjusted measures to approximate VAR in a large equity position with leverage.
I just uploaded the module to the gallery if you want to download it, but here's a picture to give you an idea (click pic to see):
Step 1 is to account for “how much selling of one’s stakes to get out of a position can cause prices to fall”. The simplest way seemed to constrain your activity to not affecting price movements. So a measure for a rough comparison is what percent of the average daily volume you can swallow without affecting the market.
Days to Exit = Position Size / (Av Daily Volume * Percent Daily Volume to Trade)
Then instead of looking at the VAR calculated by 1 day price moves, you can look at N day price moves where N = Days to Exit for large positions.
Step 2 was to illustrate how leverage affects the VAR relative to your actual invested capital. That is, if your .5% VAR is $1 million on a $9 million position that’s leveraged 3:1, it seems more pertinent to express it as 30% of your investment.
By adjusting the “Percent of Daily Volume to Trade” slider and the “Leverage” slider, you can see a comparative view of the 1 day VAR with the N-Day liquidity adjusted VAR.
The next thing I wanted to look at is how the calculated N-Day VAR compares with what’s happened historically. That is, suppose you need 4 days to liquidate a position and the theoretical percentage move for the 4-Day VAR gives you a 7% price drop. What was historically observed for 4 day windows?
To do that, I calculate the N-Day changes over the historical data, rank them, and then take the appropriate day to use for the .1% , .5%, etc. VAR measure. Based on the assumption sliders, the historical data was re-processed and ranked to recalculate the observed historical VAR for the appropriate time window. I also threw on a table with the worst 10 days just to see them in one place for a sanity check.
Since I was basing these calculations on equity trading, not natural gas futures, I used the energy company NRG for fun. The static results are interesting, but through tweaking the assumptions, I found something kind of unexpected.
When it takes only 2-4 days to liquidate, the theoretical N-Day VAR underestimates historical movements.
One explanation for this is that when people start to sell-off, the activity drives prices down even more.
However, when the number of days to liquidate is sufficiently large, the theoretical N-Day VAR overestimates the historical movements.
Again, my simple hypothesis is that there is psychology in the market when you’re looking at 5+ day downtrends. That is, stocks bounce back.
Having said that, commodities are not stocks, and the relationship described here could very well be the opposite for natural gas futures. What's important, I think, is to not blindly use a general model like N-Day VAR = Sqrt(N)*(Daily VAR) alone for volatile or illiquid positions, but to get a handle on your risk by looking at a variety of measures.
Based on this quick and dirty VAR app, I came to this conclusion: for large positions, you should incorporate a liquidity measure and probably keep both historical and theoretical VAR estimates on your dashboard.
