Risk, Volatility, Investment Return, and Risk Management

**lzhang** Tue Sep 19, 2006 12:00 am

Risk, Volatility, Investment Return, and Risk Management
Risk is often defined as a potential negative impact to an asset (value) that may arise from some present process or from some future event. So it is related to the probability of a loss. In stock market, people sometime confuse risk with volatility, the standard deviation of the change in stock price with a specific time horizon, ie, volatility is sometimes considered as the risk of stock investment. But, from a business-oriented value-investor's point of view, the risk to invest into a stock (and thus to own a small piece of business of that company), is never the volatility of the stock price. BTW, it can happen to be true for some time that the risk of the investment and the stock price volatility are equal or close to each other, but they are not the same thing, just like two apples and two oranges are two things.

In efficient market theory, EMT, which I doubt very much, (or maybe just because I do not understand it), the volatility of stock price reflects the degree of risk, because the price has correctly reflected the value of the stock, under the EMT assumption. For example, if the price drops sharply, its volatility increases (and so its risk), and the lowered price reflects the increased risk. Sounds plausible at first, but it can not stand careful scrutiny. Many people in stock market are full of emotions; people do all sorts of trading, even without knowing what the underlying business of the stock is about. How can such a mixture of people have the very right view of the business and the price set such way correctly reflect the value of the underlying business at ANY (or most) time? The EMT totally ignores the difference among the people like WEB, Peter Lynch, general public, daytraders, insiders, etc., when general public (or other people for any reason) are selling and thus pushing the price down, and those super-investors or insiders are buying. It says that price is the true value of the business. Isn't it pretty wrong? Value is a pretty subjective thing. Different people have different value for any given thing. People with great understanding in the business know more about the worth of the business, smart people and hard-working people create more value in the same business. At some time, due to unexpected negative events, or overwhelming pessimistic sentiments (people are emotional), stock price can go extremely low, and in some case, the selling is self-feeding, people are in panic mood, so how could such price be the value of the business underlying? At other time, due to unexpected positive events, or overwhelming optimistic sentiments (people are emotional again), stock price can go extremely high, and in some case, the buying is also self-feeding, so how could such price be the value of the business underlying?

I think I can understand what it says if it is stated differently, like: the market price at any moment reflects the view of people who are trading it, and it is fairly priced in a sense that sellers want to sell and buyers want to buy. Pretty much nothing in it, isn't it? But I think it is at least not misleading. On stock market, I want to quote, "In the short run it's a voting machine, but in the long run, it's a weighing machine."

So now we return to the underlying business of the stock we own. We want to keep the stock so that we have positive return over a period of time. From now on, let's forget about stock market, we do not need stock market to study the business return if we are not in the stock market related business. When we say stock in the next few paragraphs, we really mean the business. Suppose we have $1 now and want to know how much we can have with an expected yearly return of 20% for the next 30 years. If there is a such business that can guarantee 20% yearly return, we could have $1*1.2^30=$237.4 after 30 years. Too good to be true because there is no such guarantee that one can earn 20% yearly, not even 10%. So there is uncertainty on the return, ie risk, even we have estimated the return itself right. To have a feeling of what we can end up with, we have done a quick study to estimate the final return of a portfolio with 10 stocks. There are some assumptions:

1. Initial fund $1
2. Expected return is 20% yearly, which is unbiased and reflects the true value of the business
3. 10 stocks in the portfolio
4. fund equally distributed among them
5. after each year, rebalance the portfolio so that 2, 3, and 4 are true. So, these 10 stocks in the next year are not necessary same as before.
6. final performance after 30 years
7. Repeat 1, 2, 3, 4, 5 and 6 1000 times so that we can see the expected return distributions.

We have tried two different forms to model the risk. One is similar to tossing a coin model, but the difference is that we have a 80% chance each year to have positive return, and 20% chance to have negative return per stock. The risk is high when the positive return is very high and the negative return is very low (absolute value of the negative return is high), though the expected return remains the same, 20% yearly, or 1.20 the initial value. The business risk, as we define here, is the uncertainty of the business, which we quantify as the uncertainty of the expected return. The following 3 plots show the distributions for this risk model. As they all have the same expected return, the mean values of the final return for each risk group are very close to the expected 30 year return, $237.4 for $1. However the most probable value (MPV) and the spread of the distribution are quite different among the different risk groups. The histograms are fit to Landau distributions, which might not be a perfect shape for some of them, but from the plots one can see it only smears the difference so our conclusion based on the fits are very conservative. The lowest risk one has the largest MPV, and the min return, the lowest edge of the histogram, if we are hit by very bad luck, is the largest one among the three. With the largest risk, we have the worst MPV, the lowest min return of miserable $3.53 for $1 over 30 years, if we compare it with a hypothetical 5% yearly return from T-bond, which will be $1*1.05^30=$4.32, but since the distribution is so spread out that for a very slim chance we do have a return of $2198 for $1 over 30 years, which is extraordinary compared to the nominal return of $237. Is it worth to take the risk? I think as risk-averse value-oriented investor, we should avoid such situation, ie, everything else remains the same, we should take the smallest risk. Statistically the risk takers do not have any advantage, though a small percent of people can make fat profit, most of them underperform risk-averse people, with the same expected return.

The next 3 plots use a different model, where the expected returns have Gaussian uncertainties. Larger Gaussian sigma means greater risk, and basically we have the same distributions as the other model. It looks like the final return distributions are pretty risk-model independent, and depend largely on the risk size itself.

So what can we learn from this study for our real-life value investment? The real investment practice might not be modeled with such simple models, but we do have some feeling now.

As demonstrated with this study, successful investment is more than just picking a good expected return, risk control is even more critical. As we believe, the stock investment risk is not the volatility of the stock price. We mainly consider business risk as we are doing business-oriented investment. When stock price drops, the expected return increases, and if the business risk remains the same, or does not increase proportionally, we have a better chance to be successful. People will say, if the price drop 50%, we need to gain 100% to be just even. We would say, if our business view remains valid, and after 50% drop, we do have a much better expected return. If everything else remains the same, our final return will be the same. And if we are lucky enough to enter after the 50% drop, not before, our final return will be even better.

From the above study, there is no such thing called risk-premium, if the expected return is the same. With the same expected return but a larger risk associated with it, statistically people have the same final return. If one bets and takes riskier one, he has a higher chance to underperform. That might be the case for gambling and lottery players. So we want to avoid risk as much as we can.

So how can we lower the risk, the uncertainty of our business-oriented investment return? It sounds pretty tough, how can you lower the uncertainty of something, the probability of unexpected to happen? It sounds like something unpredictable, because by definition, you will never know if it can happen or not. Let's take an example outside of investment to illustrate how. For example, we know the fatality rate in (fatal) car accidents in the US is about 0.015% as of 2005. This rate can be considered as the uncertainty, the risk of life, of car-related activities. Per 10,000 people, there will be about 1.5 people died in fatal accidents in the US each year. This cold 0.015% number is pretty real, and the risk is real, so a cool fact, not something we can change. But the truth is we can change it, and furthermore, we do not even need to change the number itself, ie the national rate is still the same, but we could have a lower chance. The trick is, unlike what we think, probability is a pretty subjective thing and it is not a single number that can be put in anywhere and still be true. This 0.015% may apply to the population of the US as a whole, but when we focus the risk for a particular person, his/her risk is totally a different story. If he/she never drives a car, never rides in a car, his/her risk is very very low, maybe totally negligible. On the other hand, he/she does not enjoy the benefit of using a car, either. If he/she does drive and he/she drives carefully, never speeding, always wearing seat-belt, very protective, his/her risk is much lower than those people who are careless drivers, DUIs, etc. So now we know this risk is not a universal number correct to everybody. Let me tell another story about risk. I heard of an ads or something saying the death rate in Marine was much lower than the US as average, so US Marine was much safer than the US mainland. Sounds funny. Yeah, the US Marine did have smaller death rate, but it did not have senior people on Medicare.

The same thing for investment risk. If the investment risk can be measured as volatility of stock price, which I still do not quite believe, that risk is not applicable to everybody. An experienced investor, or a smart businessman, know much more in a particular business, so the uncertainty of their expected return is much smaller. That is why we emphasize business-oriented investment. If you do not understand the business, if you can not have a roughly correct estimate of the return, your investment is subject to huge uncertainty and the final performance is very poor. I think this is what Mr. Buffett always emphasizes. He always says if he does not understand the business, he will not invest into the business.

If we understand the business, understand the company, now the question is when to buy. If the risk is known to us, the only question is how much we want to pay. We want to pay as few as we can! If someday, for some reason, Mr. Market offers us with attractive price, we certainly will buy. If Mr. Market is very pessimistic and offers a much lower price than usual, we will be very glad to accept it because we know our expected return will be much higher; if Mr. Market is very optimistic and offers a very high price to buy, we will be very glad to sell our holdings, because we know our expected return will be much lower, in which case it is not worth to hold.

Original post @ http://hepinvestor.blogspot.com/2006/09/risk-volatility-investment-return.html

Ref links:

http://en.wikipedia.org/wiki/Risk

http://en.wikipedia.org/wiki/Risk_management

http://en.wikipedia.org/wiki/Volatility

http://www-fars.nhtsa.dot.gov/
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**blast_investor** Wed Sep 20, 2006 12:03 pm

Hi lzhang,

Excellent modeling work.

Your quantitive modeling essentially support the theory behind value investing.

The whole point of value investing is to find pick to enhance the risk control and increase the odds.

The exact approach of value investing are well known and could be different, low price book (or replacement cost), owner's earning, return on asset, etc, high insider buying. All these metrics are used to increase odds on risk control.

The more portfolio can do that risk control, the higher the overall return will be in the long run.

**blast_investor** Wed Sep 20, 2006 12:31 pm

Hi lzhang:

The the individual odd issue. I believe value investing method has high odds. I don't know of any research on this issue.

However, we do know that the best value investor Warren Bufffet, his odds in the past have been very high.

For any past 100 picks Buffett invested over past decades, he only managed to lose money in 1 pick, and 99 picks he made money out of it in his holding time period. That is 99% of odds.

**lzhang** Wed Sep 20, 2006 12:45 pm

Hi blast,

WEB's case is exceptionally great and I do not think we should take it as a general case. His success is based on his exceptional vision into the business and he invests only if he understands the business. Most importantly, he is following the business-like value investement practice.

But in general, value-investement, by its nature, has low risk. And in cases, which may be rare, but still exist due to the madness of the stock market, that the price is below NCAV or book value, the risk is extremely low.

Even EMT believers now admit that value-investement, as a whole, outperforms other methods. I think this argument is backed up with their own published academic papers.

So by choosing the right method itself, the odd is already on your side.

blast_investor wrote: Hi lzhang:

The the individual odd issue. I believe value investing method has high odds. I don't know of any research on this issue.

However, we do know that the best value investor Warren Bufffet, his odds in the past have been very high.

For any past 100 picks Buffett invested over past decades, he only managed to lose money in 1 pick, and 99 picks he made money out of it in his holding time period. That is 99% of odds.

**blast_investor** Wed Sep 20, 2006 3:07 pm

Hi lzhang:

I totally agree with you.

Value investing is the best kept secret in stock market.

I am not sure EMT theory admits that value investing can out-perform the market. If they did that, that is in odds with EMT theory. EMT believes in market effciency. If market is so effcient, it is hard to admit that there is a method that can beat market.

lzhang wrote: Hi blast,

WEB's case is exceptionally great and I do not think we should take it as a general case. His success is based on his exceptional vision into the business and he invests only if he understands the business. Most importantly, he is following the business-like value investement practice.

But in general, value-investement, by its nature, has low risk. And in cases, which may be rare, but still exist due to the madness of the stock market, that the price is below NCAV or book value, the risk is extremely low.

Even EMT believers now admit that value-investement, as a whole, outperforms other methods. I think this argument is backed up with their own published academic papers.

So by choosing the right method itself, the odd is already on your side.

**lzhang** Wed Sep 20, 2006 3:30 pm

That is from the book, A Random Walk Down Wall Street by Burton Malkiel, who is a leading proponent of EMT. In his latest edition (before 2006), he quoted a paper that by some studies, the value-oriented investment outperformed the market. So he continued, tried to look for some value. I did not remember clearly what paper he quoted and what was his remarks on that because I did not have the book with me now.

blast_investor wrote: Hi lzhang:

I totally agree with you.

Value investing is the best kept secret in stock market.

I am not sure EMT theory admits that value investing can out-perform the market. If they did that, that is in odds with EMT theory. EMT believes in market effciency. If market is so effcient, it is hard to admit that there is a method that can beat market.

lzhang wrote: Hi blast,

WEB's case is exceptionally great and I do not think we should take it as a general case. His success is based on his exceptional vision into the business and he invests only if he understands the business. Most importantly, he is following the business-like value investement practice.

But in general, value-investement, by its nature, has low risk. And in cases, which may be rare, but still exist due to the madness of the stock market, that the price is below NCAV or book value, the risk is extremely low.

Even EMT believers now admit that value-investement, as a whole, outperforms other methods. I think this argument is backed up with their own published academic papers.

So by choosing the right method itself, the odd is already on your side.