Exhibit 4 Reading 41

[Atomic_Sheep]

Hi,

I’m examining exhibit 4 and its observations. The books say:

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I don’t understand the first sentence.

Also:

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Am I interpreting the second sentence correctly? If we pick a stock at random each quarter, record its return then do this for all subsequent quarters and if you run this experiment many times, you will get an annualised return of 15.1% and a sd of 24.9%?

3.) Finally, I don’t understand the heuristics used to come to this conclusion, to me this doesn’t seem apparent/obvious:

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(Institute 239)

Institute, CFA. 2016 CFA Level I Volume 4 Corporate Finance and Portfolio Management. CFA Institute, 07/2015. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

[S2000magician]

@Atomic\_Sheep

1.) “However, if there is no reason to believe that the future will replicate the past, it is more likely that the risk and return on the one security selected will be more like selecting one randomly.”

Suppose that you have three stocks: A, B, and C. If you expect that history will repeat itself, then you can use that information to guide your stock selection each quarter (e.g., if A’s return has been higher than B’s return with the same volatility, you’ll choose A instead of B). If you have no reason to believe that history will repeat itself, then you have no information to bias your selection: whatever you choose, on average, will be the same as choosing the stocks randomly.

@Atomic\_Sheep

2.) “When we randomly selected one security each quarter, we found an average annualized return of 15.1 percent and an average annualized standard deviation of 24.9 percent, which would now become your expected return and standard deviation, respectively.”

Am I interpreting the second sentence correctly? If we pick a stock at random each quarter, record its return then do this for all subsequent quarters and if you run this experiment many times, you will get an annualised return of 15.1% and a sd of 24.9%?

It says that that’s what your expected return and standard deviation of returns are. What you actually get could be much different. Just as with rolling a fair die: your expected value is 3½, but, for whatever reason, you never _ actually roll _ a 3½.

@Atomic\_Sheep

3.) Finally, I don’t understand the heuristics used to come to this conclusion, to me this doesn’t seem apparent/obvious:

“As reported in Exhibit 4, the equally weighted portfolio has an average return of 15.1 percent and a standard deviation of 17.9 percent. As expected, the equally weighted portfolio’s return is the same as the return on the randomly selected security. However, the same does not hold true for the portfolio standard deviation.”

All they’re saying is that the standard deviation of returns of a portfolio is not the weighted average of the standard deviations of the constituent securities: there’s a diversification benefit.

[Atomic_Sheep]

Ah it’s one of those complify simplicated situations. I’m doing the opposite. Just need to use the simple arithmetic average. I’m taking it in a whole nother direction. I think I need to review independence and dependence, I have a feeling I don’t understand basic maths.