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Chapter 6: Efficient Diversification

General thought: Risk comes from different places. Some risk comes from common sources, like the economy. Other risk comes from sources unique to each asset. This means that some kinds of risk can be diversified.

Return and Risk for a Portfolio

0 First, need to know how much you’ve invested in each asset (w) as a percentage of your total funds invested.

Expected return on a portfolio

In other words, portfolio expected return is always a weighted average of the expected returns of the assets within the portfolio.

However, this is not true of portfolio standard deviation!

* Portfolio standard deviation depends on covariance / correlation between each pair of assets within the portfolio…how much the movements between each pair of assets offset each other.

* In general, portfolio standard deviation will be less than the weighted average of the standard deviations of the individual assets within the portfolio.

1 Covariance =: Tells you how much any pair (two) stocks (i and j) move around together:

| Prob. | 1 | 2 | Great | .3 | .2 | .1 | OK | .5 | .1 | .2 | Bad | .2 | - .05 | .4 |

= -.0033 + 0 + -.0057 = -.009

Correlation between Two Assets

The correlation coefficient “standardizes” covariance – puts it into a form that tells you how much two assets actually move together. Correlation coefficients are scaled between –1 and +1:

= = -.995

Finally, we can use covariance to tell how risky the entire portfolio is …

Variance of a portfolio

If N=2,

If N=3,

Last step: Take square root of variance to get standard deviation.

Why are combinations of two risky assets concave?

* Depends on extent of correlation between assets making up the portfolio … Assume that we have two assets (1 and 2), and the extreme cases of perfect

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