1. Home
  2. Financial Planning
  3. Value at Risk (NYT article)

Value at Risk (NYT article)

Prompted by the financial crisis, the latest New York Times magazine has a long article "Risk Mismanagement" by Joe Nocera

formatting link
about the use(some argue misuse) of the Value at Risk (VaR) measure by financialinstitutions. A 99% VaR of $100 K for a 1 month time horizon is aforecast that 99% of the time, the loss on a portfolio will be lessthan or equal to $100,000. The article notes a defect of VaR -- itsays the losses in the worst 1% of scenarios will be worse than acertain amount (in this example $100 K), but it ignores how much worsethey could be.

A risk measure called "expected shortfall" is defined to be the expected loss for a specified time horizon and quantile (such as 1 month and 1%). Unlike VaR, it does depend on the magnitude of the losses in the left tail. The Wikipedia article

formatting link
it and presents examples of its calculation. Researchers inrisk management generally consider it a better risk measure than VaR,and I wonder why the NYT article does not mention it in a ten-pagearticle.

Risk measure are relevant to individual investors as well as investment banks. Given a method of simulating returns (either drawing from historical returns or using a parametric distribution such as the normal), one can estimate the expected shortfall of an investment strategy in meeting some liability. For example, one could estimate the expected shortfall from investing a $50K lump sum in the stock market for 10 years and selling 25% of the portfolio over each of the next 4 years in order to pay annual college expenses of $25 K. One would need a distribution of stock market returns, perhaps normally distributed with annualized mean of 8% and standard deviation of 16%. Currently, financial planning software usually quantifies risk by forecasting the probability of an investment strategy succeeding, for example the probability of not running out of money over 20 years given an initial withdrawal of 4% of the portfolio, increased annually at the rate of inflation. This risk measure, like VaR, ignores the magnitude of the failure when the failure occurs. It treats running out of money in year 5 and year 19 as the same. An expected shortfall measure may be better.

Reply to
beliavsky
Loading thread data ...

Asking your indulgences, with an eye to a happy start to a new year, a little humor from the farm ....

The other day, I saw a duck crossing the road. Curious about this, because I thought only chickens crossed roads, I ambled over and got a rare exclusive interview with the duck. "Chickens are talked about," he explained, "because they're hit by speeding tricycles more often. Us ducks hardly ever get hit." "Are chickens dumber than ducks?" I asked. "Oh, no!" the duck said, "They're much smarter, and have PhD's in mathematics!" Puzzled, I asked, "Well, if chickens are smarter, how come they get hit more often?" The duck smiled. "They use probability theory and virtual risk management models. Then they strut around in circles, and never see the actual tricycle that creams 'em. We ducks are taught to look both ways before making our next move, and walk in a straight line."

Reply to
dapperdobbs

The article that beliavsky cited is, in fact, very interesting and well researched, as are most NY Times articles these days.

At the core of the issue is that Value at Risk metric assumes that asset returns are normally distributed and their correlations are knowable and do not change much. The article expounded quite a bit on the former (normal distribution), citing Nassim Taleb and other luminaries in debunking the idea of normally distributed returns. Which is quite correct.

What I would like to do is to attract attention to the second issue, which is correlations.

As a result of assuming that correlations are knowable and do not change, the risk of a portfolio comprised of various such assets, was estimated to be considerably lower than the risk of owning one such asset, due to those correlations. For example, the returns of Ukrainian state debt would be not too correlated with portfolios comprized of Arizona Alt-A mortgages. So if you mix Arizona mortgages with Ukrainian debt, you could get decent return but low value at risk. So your VaR analysis told you that it would be a relatively safe thing to do to borrow some money, using these assets as colateral.

As we now know, that was not the case and they all were subject to credit risk. In the crisis, as we heard, "all correlations went to 1" and all sorts of securities started losing money in tandem. Which was a mathematically impossible event, under assumptions of wrong models used.

Unlike those giddy times, now everyone is afraid of everything, and it is a great time to invest prudently (not using too much leverage).

i
Reply to
Igor Chudov

Value at Risk and Expected Shortfall can be estimated for return distributions other than the normal distribution, as discussed in a paper "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES" at

formatting link
. Taleb specializes in attacking straw men.

Reply to
beliavsky

Nocera

formatting link
the use> (some argue misuse) of the Value at Risk (VaR) measure by financial > institutions.
formatting link
is referenced in the article andgives a better insight into the problems of risk analysis. Risk is relative because we don't know when the very unusual things will occur.

Conventionally, investors are asked to split their investment between stocks and bonds. If this were to be done using only S&P 500 stocks and bonds, the average investor would be only 25% into bonds since those companies aren't highly leveraged.

-- Ron

Reply to
Ron Peterson

Can you explain this? Why 25%? Where'd that number come from? Joe

Reply to
JoeTaxpayer

It's a shirt-sleeve calculation based on the average debt to book ratio and average price to book ratio of the S&P 500 stocks.

Much financial debt comes from government obligations and home loans so I am not sure what the entire investing universe looks like.

-- Ron

Reply to
Ron Peterson

I'm with Joe on this one and I'm still confused. How do you get from debt/book and/or P/B to allocations of stocks vs. bonds?

-Will

william dot trice at ngc dot com

Reply to
Will Trice

I think what he is saying is that if you invest in only securities issued by the S&P 500 companies, both stocks and bonds, and weight your investments on the total market value of the securities (like an index fund but including the bonds in addition to the stocks), then for example:

If the aggregate capital structure for these companies is 40% debt and

60% equity The market value of the debt is 100% of the book value (i.e. trading at par) The market value of the Equity is 200% of the book value. The total market values of the companies' securities would be 160% of their book value, of which stocks would be 75% and bonds 25%.

So if you weight according to market values, you would be 75% in stocks and 25% in bonds.

There is an implicit assumption that all the debt is publicly traded.

Reply to
themightyatlast

Come again? How did market value of equity become 200%? You haven't said anything about stock price here. I'm probably just being obtuse...

I'm just guessing, but I'd think that the market value of all the debt of all the S&P 500 companies is larger than the market value of all their shares, so you probably have your allocation backwards.

-Will

william dot trice at ngc dot com

Reply to
Will Trice

According to Reuters the P/B ratio for the S&P 500 is 6.84 and the total debt to equity is 197.45%. So the ratio of equity to debt is

3.46.

-- Ron

Reply to
Ron Peterson

Ron, the numbers are a little surprising, can you point me to some website by Reuters that says what you are citing? Thanks

Reply to
Igor Chudov

See

formatting link

-- Ron

Reply to
Ron Peterson

Yes, and I see 2.90 price to book for S&P 500.

Reply to
Igor Chudov

Sorry. All my numbers were made up. I was just showing how the numbers are mathematically related.

Reply to
themightyatlast

You're looking at the price to book for the technology sector that IBM is in, not the S&P 500.

-- Ron

Reply to
Ron Peterson

Probably still being obtuse, but if debt to equity is 197.45% then equity to debt (the inverse) would be 50.646%, right? What's P/B got to do with it?

-Will

william dot trice at ngc dot com

Reply to
Will Trice

That is book debt to book equity. Book equity is 50% of book debt. But market equity is 6.84 times book equity (that is what P/B has to do with it). So the market value of equity is 3.46 times the book value of debt. If the market value of debt is equal to the book value of debt (not an unreasonable approximation for S&P 500) then the ratio of market value of equity (market cap) to market value of debt is 3.46 to

1.
Reply to
themightyatlast

BeanSmart website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.