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Session 6. How Much Risk To Bear
Other people will pay you to bear risk. But
this risk premium will be most advantageous for you only if you know how to
judge how much risk you can afford to shoulder at any one time. (It is
also necessary for you to efficiently diversify among offsetting risks, so that
you bear no unnecessary risks, but that is another topic.)
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Source: US Dept. of Agriculture |
Risk has to do with the chance of catastrophe.
If I am living solely on income from my investments, catastrophe is
losing enough money so that my living standard will be reduced to
unacceptable poverty. Even a loss of only 30% may do it. On the other hand,
for a young person on salary, losing even more than 100% of his or her meager
savings may not be a catastrophe, because the amount was small relative to
employment compensation in the first place and can be replaced
with minor adjustments in savings rates.
Consider a professional gambler. For him, catastrophe is losing exactly
100% of
his stake, or capital, because that is sufficient to put him out of the game. Although it is not taught in the usual
investment textbooks, there is a formula (the Kelly criterion) that can be very
helpful to a gambler in deciding how big a bet to take at each point
in time. It maximizes the expected long-term growth rate in his stake.
The inputs to the formula are:
- the size of his stake (positive impact)
- the odds (average profit) on each bet (positive
impact).
It is pretty clear that if each bet has an average loss, it is not a
terrific idea to bet anything. With repeated bets eventually I will lose
everything! But it may be surprising to note that
if the bets are too large relative to the size of my stake, I
will eventually lose everything even if the average outcome per bet is
favorable!
Consider a game in which you decide each bet is for your entire stake. Two-thirds of the times
in which you bet, you will double
your money. But if you lose, you lose everything. The average return per
bet is 33%. Sounds great. But
after enough bets, you will always lose everything. Hmm. Not so
great. Maybe you could do better if you didn't bet your entire stake on
each outcome ....
In this simplified example, the Kelly rule reduces
to betting one-third of whatever stake you have just before each bet. If you bet more, you will damage your
future by tending to dip too far into capital on losing streaks. If
you bet less, your winning streaks will not take full advantage of the
opportunity offered by the favorable odds. The expected compound return from the
best strategy in the example is about 10% of total capital at each turn. This is
a lot better than a sure eventual loss of everything.
This principle of maximizing expected compound return by not betting
everything on one toss of the coin carries directly over to how much of your assets should be invested in riskier
stocks (your bet) as opposed to less risky bonds and cash. If you are
retired and a loss of
capital of 30% represents the loss of your entire discretionary stake, you would be wise
not to place as big a bet on stocks relative to your total wealth as should a
younger person, because you may well get knocked out of the game.
A sophisticated approach to setting your best
allocation between stocks and bonds or cash, based on the Kelly rule and a
concept of discretionary wealth, is noted in the "professional" learning section
and in more detail in the research paper "Better Risk Management" in the
resources section of this website. Savers without this kind of analysis
might do worse than to check out the overall recommendations of a mutual fund
company, such as Vanguard, or pay a modest
fee to Financial Engines.
Many investors who seek financial advice end up with a portfolio about 60% in
stocks and 40% in various kinds of safer securities, but what is best for you
will depend on your age, goals and various specific circumstances.
Risk interferes with the typical compounding of
returns. It can cause a catastrophe if not properly managed. Yet if
you don't take enough risk, you may not earn a high enough return to meet your
investment goals. The key concept of this session is that each
investor has a balance point that will give him or her the best available
long-term growth and income path while avoiding catastrophe.
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