4 ms·

Diversification only lowers risk. The expected value doesn't change.

vasilipupkin 12y ago
Sir/Madam, that is incorrect. Diversification can easily lower expected value, or raise it. It should maximize your signal to noise ratio, if properly done.
- msellout 12y ago
  You're using a different definition than the one I learned in school. The purpose of diversification, as opposed to simply picking the best asset, is to decrease variance. Given a choice between two assets, or portfolios, one first maximizes expected value. Between two portfolios of equal expected value, you pick lower variance. That's the rational thing to do if you are managing a fund. The whole risk ratio thing arises only because so many investors are trying to build a well-diversified portfolio and bid up or down the price of assets accordingly. Price in turn affects expected return -- the expected value of the asset.
  - vasilipupkin 12y ago
    My point is simply that diversification results in a different expected return of the final portfolio. Before diversifying your expected return was R1 and after it will be R2 where R1 != R2. So, for choosing startup vs big co, or one startup vs another, this is relevant as well.
- imh 12y ago
  I believe the definition they are using is something like: given a random process X for your percent return, if you invest in n nths of your money into iid copies of X, you will get the same expectation, but with smaller variance compared to putting it all into one copy of X. That's diversification.
foobarqux 12y ago
Which matters a lot if you only have one or two shots.
- deleted 12y ago
  [deleted]
throwaway183839 12y ago
Everyone has a personal tolerance for risk. If you are diversified, then you decrease the risks that you are exposed to - possibly below your personal risk tolerance. That allows you to use leverage to increase your risk back up to your tolerance, which also increased your expected return. So yes, diversification (plus leverage) absolutely increases expected value, if you hold risk a constant.
DavidSJ 12y ago
Given diminishing marginal utility of wealth, diversification increases expected utility, even if not expected wealth.
defen 12y ago
Would you rather have a 1% chance at a billion dollars or a guaranteed million? The former has a 10x higher expected value but I think most people would choose the latter.
- TTPrograms 12y ago
  I love examples like this. My interpretation of this generally depends on an idea of "Expected Impact", where ex. the difference between $10^6 and $10^9 in terms of lifestyle impact can be smaller than the difference between $10^3 and $10^6. You could assume a logarithmic value function, for example, but each person might have a different function depending on what you would do with the money. Not that people actually think that way, but you can construct a model where the guaranteed million is the rational choice.
  - markpundmann 12y ago
    What your talking about is commonly referred to in economics as diminishing marginal returns. The first $1000 is much more useful than the second. Also, your interpretation of "expected impact" is what we call economic utility, which is commonly put in a cobbs douglas utility function (utility = (some_number > 1)^(1 > some_number > 0).

Sir/Madam, that is incorrect. Diversification can easily lower expected value, or raise it. It should maximize your signal to noise ratio, if properly done.

msellout 12y ago
You're using a different definition than the one I learned in school. The purpose of diversification, as opposed to simply picking the best asset, is to decrease variance. Given a choice between two assets, or portfolios, one first maximizes expected value. Between two portfolios of equal expected value, you pick lower variance. That's the rational thing to do if you are managing a fund. The whole risk ratio thing arises only because so many investors are trying to build a well-diversified portfolio and bid up or down the price of assets accordingly. Price in turn affects expected return -- the expected value of the asset.
- vasilipupkin 12y ago
  My point is simply that diversification results in a different expected return of the final portfolio. Before diversifying your expected return was R1 and after it will be R2 where R1 != R2. So, for choosing startup vs big co, or one startup vs another, this is relevant as well.
imh 12y ago
I believe the definition they are using is something like: given a random process X for your percent return, if you invest in n nths of your money into iid copies of X, you will get the same expectation, but with smaller variance compared to putting it all into one copy of X. That's diversification.

foobarqux 12y ago

Which matters a lot if you only have one or two shots.

deleted 12y ago
[deleted]

throwaway183839 12y ago

Everyone has a personal tolerance for risk. If you are diversified, then you decrease the risks that you are exposed to - possibly below your personal risk tolerance. That allows you to use leverage to increase your risk back up to your tolerance, which also increased your expected return. So yes, diversification (plus leverage) absolutely increases expected value, if you hold risk a constant.

DavidSJ 12y ago

Given diminishing marginal utility of wealth, diversification increases expected utility, even if not expected wealth.

defen 12y ago

Would you rather have a 1% chance at a billion dollars or a guaranteed million? The former has a 10x higher expected value but I think most people would choose the latter.

TTPrograms 12y ago
I love examples like this. My interpretation of this generally depends on an idea of "Expected Impact", where ex. the difference between $10^6 and $10^9 in terms of lifestyle impact can be smaller than the difference between $10^3 and $10^6. You could assume a logarithmic value function, for example, but each person might have a different function depending on what you would do with the money. Not that people actually think that way, but you can construct a model where the guaranteed million is the rational choice.
- markpundmann 12y ago
  What your talking about is commonly referred to in economics as diminishing marginal returns. The first $1000 is much more useful than the second. Also, your interpretation of "expected impact" is what we call economic utility, which is commonly put in a cobbs douglas utility function (utility = (some_number > 1)^(1 > some_number > 0).