# Why diversify?

I know that diversifying is so that some event can’t wipe out the whole investment, but why diversify?

Or is the higher expected return: standard deviation the rationale behind diversification?

How can diversification reduce the portfolio’s standard deviation without reducing the expected rate of return of the portfolio?

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I don’t think you can have both. You will reduce SD and expected return. When you reduce risk, you reduce returns.

Atomic_Sheep wrote:
I don’t think you can have both.

Of course you can.

Atomic_Sheep wrote:
You will reduce SD and expected return. When you reduce risk, you reduce returns.

Not necessarily.

Y’all have heard of efficient portfolios, yes?

Simplify the complicated side; don't complify the simplicated side.

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I was thinking of a scenario where you have say 100% in an asset A with Er = 15% and SD of 17% and then you diversify to a portfolio of 50% asset A and 50% in asset B which is say Er = 10% and SD of 8% and a Cov(0.5). You get an ERp of 12.5% and a SDp of 11.36%. In this case, you can’t reduce your risk and increase/keep your return.

P.S. I need to revise my SDp calculation because I’m not able to get 11.36%, I’m getting 55% for some strange reason, need to figure out where I’m making the mistake. I just used this site for the 11.36% value: http://www.zenwealth.com/businessfinanceonline/RR/PortfolioCalculator.html

Will spend some time trying to figure out where my mistake was.

So as you see, you can’t reduce your risk without reducing your return.

The principle of Modern Portfolio Theory is that having just one stock (instead of many) wont necessarily give you better returns. Having a diversified portfolio will help you reduce your risk and grow your profitability.

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Atomic_Sheep wrote:
I was thinking of a scenario where you have say 100% in an asset A with Er = 15% and SD of 17% and then you diversify to a portfolio of 50% asset A and 50% in asset B which is say Er = 10% and SD of 8% and a Cov(0.5). You get an ERp of 12.5% and a SDp of 11.36%. In this case, you can’t reduce your risk and increase/keep your return.

P.S. I need to revise my SDp calculation because I’m not able to get 11.36%, I’m getting 55% for some strange reason, need to figure out where I’m making the mistake. I just used this site for the 11.36% value: http://www.zenwealth.com/businessfinanceonline/RR/PortfolioCalculator.html

Will spend some time trying to figure out where my mistake was.

So as you see, you can’t reduce your risk without reducing your return.

One example doesn’t prove a general statement.

Suppose that you have 100% of your portfolio invested in asset A which has E(r) = 10% and σr = 8%.  You add asset B which has E(r) = 16% and σr = 12%, where ρA,B = −0.1.  A 50-50 A/B portfolio has E(r) = 13% and σr = 6.87%.

So as you see, you can reduce your risk without reducing your return.  In fact, you can reduce your risk while increasing your return.

Simplify the complicated side; don't complify the simplicated side.

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Hmm fair enough. More study of diversification is in order.

If you have two assets that are perfectly correlated, the standard deviation of the portfolio will be the weighted average of the standard deviations the two assets.  If it’s less the correlation between the two is LESS than one, the portfolio SD will be less than the weighted average of the individual SDs.

Here’s another example:  Assume you have two Assets (A and B) that both have expected returns of 10% and SDs of 20%.

A portfolio of the two will always have an expected return of 10% (the average of 10 and 10 is 10). However, the SD of the portfolio depends on the weights AND the correlation between the two assets.  If the two assets are perfectly correlated, ANY portfolio weights will also give you an SD of 20%.  If the correlation between the two assets is less than one, the portfolio will have a SD less than 20%.  Try it with an excel spreadsheet and the portfolio SD formula, pick weights, and vary the correlation coefficient, and see for yourself.

In the extreme case (a correlation of -1), a 50/50 portfolio will have the same 10% return and a SD of ZERO (i.e. it becomes a risk-free portfolio).

So you can get diversification without decreasing return.  Combining an asset with another that has a HIGHER return means the portfolio will have a HIGHER return, and combining an asset with another that has a LOWER return results in the portfolio having a LOWER return.   But the effect on Std Deviation depends on both the standard deviation of the new asset and (just as important) its correlation.

As you have a portfolio with multiple assets, the effect that adding a new of asset has on portfolio SD becomes increasingly driven not by the new assets SD, but by its average correlation with all the other assets in the portfolio.

You keep using that word.  I do not think it means what you think it means.

To add to the detailed explanations above, diversification is important not only in a linear setting (e.g. hedging) but in a non-linear setting as well. Think of a basket call option on a portfolio of assets 1, …, N. The basket option will always be cheaper than the corresponding basket of vanilla options because

$\max(x_1 + x_2 + ... + x_N, 0) \leq \max(x_1,0) + \max(x_2,0) + ... + \max(x_N,0).$