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A value-at-risk model basically works like this. You have some stuff, which is worth X today. Tomorrow it will be worth X + Y, where Y ranges from more or less negative infinity to positive infinity. Y is a function of a bunch of correlated random variables, rates and credit and stock prices and general whatnot. You look at a distribution of moves in those variables and take (usually) a 2-standard deviation daily move; if 95% of the time rates move by -10 to +10 basis points, your VaR model will assume a -10bp or +10bp move, whichever is bad for you. You take the 95%-worst-case, taking into account correlation etc., and tot up how much you’d lose in that case. Then you write that number down and feel a bit better, since you’ve sort of implicitly replaced “we have $X today and will have some number between negative and positive infinity tomorrow” with “we have $X today and will have some number between ($X – VaR) and positive infinity tomorrow,” though of course the first statement is true but unhelpful and the second is *not* true and also unhelpful.

But that aside! You get your VaR from a distribution of your variables, but the obvious question is *what* distribution. A good answer would be like “the distribution of those variables over the next three months,” say, for quarterly reporting, but of course that is only a good answer because it begs the question; if you knew what would happen over the next three months you would, one assume, always end those three months with more than $X and this VaR thing would be moot or moot-ish.^{1}

So instead you look at things that you think will allow you to predict that future distribution as accurately as possible, which is epistemically troubling since VaR is a measure of how inaccurate your predictions might turn out to be. Anyway! You pick a distribution of variables based on the sort of stuff that you always use to estimate future distributions in your future-distribution-estimating business, which could mean distributions implied by market prices (e.g. option implied vol) but which seems to mostly mean historical distributions. You look at the last N days of data and assume that the world will be similarly distributed in the following M days, because really what else is there to do.

Picking the number of days to use is hard because, one, this is in some strict sense a nonsense endeavor, but also two, the world changes over time, so looking back one year is for instance rather different from looking back four years. Here is how different:

That’s a graph of volatility in S&P 500 and 10-year Treasury rates over the previous three months on each day in the last five years; note the particular unpleasantness right around four years ago.^{2} If you had $1 billion of S&P 500 stocks today and you calculated a VaR based on last year’s data you would use about a 16.5% volatility, leading to about a $21 million possible one-day loss. If you used the last four years’ data you’d have 28% volatility, or $35mm possible loss.^{3}

I use one and four years because the FT’s Tracy Alloway is reporting that Morgan Stanley changed its VaR model from using a four-year lookback to a one-year lookback, resulting in this:

So Morgan Stanley’s daily risk decreased from $82mm to $63mm by changing the model, a 23%-ish decrease.^{4} As Ruth Porat said on the earnings call this morning, this lets them be “more responsive to current conditions while maintaining a long-term perspective,” but of course if they wanted to change it back they could do so in order to “have a longer-term perspective while remaining responsive to current conditions.”

One important conclusion to draw here is NOTHING, there is no conclusion, don’t draw conclusions. In the specific sense that an easy reaction here is:

- Morgan Stanley changed its models to use the last relatively
^{5}benign year of data instead of the last horrifying four years of data - This made it look about 23% safer than it previously looked.
- It convinced regulators to sign off on this change in the model, which flows not only to the VaR report you ignore in the earnings supp but also into things like Morgan Stanley’s capital requirements and, thus, its cushion against blowing up.
- LIES!
- etc.

All of that is true except the LIES! and maybe the etc. Or I mean it’s true but trivial: yes, VaR is lies, and it was lies before they changed the model and it’s lies afterwards, and you can get furious at it and many people do, but *if* you have a world where VaR is a thing, and a thing that affects things like capital requirements, then you are tasked with making it not just a maximally conservative thing but a good thing. There is no obvious (to me) reason that one year is better or worse than four years. Maybe the next year will be as placid (heh) as the last. Maybe it will be more placid. Maybe everything will improve smoothly forever and this current VaR model will look absurdly conservative. Maybe the horse will talk.

Four years is of course *more conservative* than one year (now – the opposite was true in 2009), but it’s also less conservative than just, for instance, calibrating your VaR models to 2008 data forever. You can be conservative to any arbitrary level; the whole game of VaR and capital requirements and investment banking and everything else is that they are *something other than maximally conservative*. If you want to be maximally conservative, don’t trade bonds, y’know?

Interestingly that is *kind of* Morgan Stanley’s long-term strategy. We’ve talked before about Morgan Stanley’s slow mosey from investment banking and trading to wealth and asset management, and it continues unabated; James Gorman kicked off the earnings call with praise for wealth management margins and its centrality to the future. Changing risk models to show lower risk-weighted assets and thus higher capital levels is all the rage this earnings season; Jamie Dimon got on JPMorgan’s call and said “we have changed our risk model so we can be more thinly capitalized and buy back stock, you gotta problem with that?”^{6} On Morgan Stanley’s call this morning an analyst asked Gorman a question about what he was planning to do with an improved capital position and the answer was in essence “buy more of the Morgan Stanley Smith Barney joint venture until we own all of it.”

If you are going to reprogram your computers to make you look safer and free up cash, I suppose using that cash to buy a steady stream of fee-based 30%-margin retail earnings is better than just flinging it back at shareholders? Or worse, I don’t know, very possibly worse, but “better” in the sense of “maximally conservative.”^{7}

A tale of two VaRs [FTAV]

Morgan Stanley posts higher adjusted earnings [Reuters]

Morgan Stanley Shows Strength in Quarter [DealBook]

Bond business lifts Morgan Stanley [FT]

Earnings Release – Financial Supplement – 8-K [EDGAR]

1. *This is an approximate description of Goldman Sachs in some (pre-2007) periods. [ Update: Good exercises for the reader include (1) explain why knowing the future distribution does not in fact mean that you will always make a profit, (2) explain how it could if you so choose allow you to guarantee a profit, and (3) explain why you might choose not to do that.]*

2. *Treasury yields not prices, which is why Treasuries look more volatile than stocks.*

3. *This uses different numbers from the graph: the graph is 3-month historical vol on each day; the calculations are just Bloomberg SPX <index> HVT using 260 and 1040-day historical vol as of today. 260 days = a conventional trading year. The math here is (1) vol is a one-standard-deviation yearly move, (2) vol goes with square root of time so conventionally one-day vol is 1/16th (i.e. ~1/sqrt(260)) of annual vol, (3) and we want a two-standard deviation-move. So 16.5% x 1/16 x 2 x $1bn = $20.6mm, etc.*

4. *But its equity price VaR decreased from $32mm to $26mm, an under-20% decrease, as opposed to a pure-S&P-500-portfolio VaR, which I calculated in the text as 56% to 33% i.e. a 41%-ish decrease. Exercise for the reader: is that, like, gamma effects, differences between long and short position VaRs, MS’s equity positions being low beta, use of something other than straight 1 vs. 4 year data (e.g. implieds?) in equity VaR model, other?*

5. *Relatively!*

6. *Though possibly I was the only person who heard that last part.*

7. *There are other non-conclusions worth drawing here too. For one thing, banks continue to be as much bundles of accounting and modeling decisions as they are bundles of economic actions. I’ve in the past made efforts to compare the big banks on revenue-to-VaR efficiency, attempting in some loose way to separate performance that comes from risk-chasing from performance that comes from smartness and/or client flows or whatever. That seems sort of embarrassing now, doesn’t it? Any performance separation is surely confounded by model differences; old-VaR Morgan Stanley was a laggard but new-VaR Morgan Stanley is a star even though they’re the same Morgan Stanley.*

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First post of the day was a Matt post.

It's going to be a long day.

I prefer 23% more wafer.

Matt, it's okay, just let it out – we're all totally cool with an explosion of charts showing how you could outsell the living shit of that pussy Greg Smith when it comes to derivatives and if he thinks changing your outlook on something a dozen times is impressive he better get ready for ************************************

Fuck Matt, I missed my shower timing window for this shit. Damnit.

It appears MS and the FDIC are currently fucking, and a more boring MS is the result.

In re the Horse: "I was reminded of this story because I'm watching an internal presentation where somebody told this same story, except a) It took them 7 1/2 minutes, not the 20-30 seconds it would take to tell my version above"

MATT: SEE ABOVE

A donkey molested me once, twice in a row.

-G. Smith

Thank you for explaining to me what nobody would explain to me for the past 4 years.

– CRM Ops

but less vol = more cash <> more bonus

<img src="http://memecrunch.com/meme/AZDN/i-rarely-think-about-changing-my-var-model/image.png"/>

I just googled google to find out what happened.

– R.R. Donnelly Risk Quant

Barclays Trader 1: "What's the call on the LIBOR?"

Barclays Trader 2: "LIBOR is X% today and will be some number between negative and positive infinity tomorrow"

I am introducing a new ETF that uses futures to hedge generic I bank VaR.

Big futures guy.

VaR is like herpes

On footnote 3, I thought a conventional trading year was 252 days?

If anyone needs help understanding VaR, please contact me.

<img src="http://www.newautoquote.us/ikeas/loo.jpg"/>23% safer? how'd they even come up with that obscure number? <img src="http://www.newautoquote.us/xboz/jj.jpg"/>

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