###
**CFA Practice Question**

As the number of securities in a portfolio increases, the portfolio variance ______.

II. depends more on average covariance

III. depends more on average expected value

IV. depends more on average variance

I. decreases

II. depends more on average covariance

III. depends more on average expected value

IV. depends more on average variance

Correct Answer: I and II

###
**User Contributed Comments**
19

User |
Comment |
---|---|

examinee |
I need not be true. It depends on the profile of the securities. |

phillip |
I is true. As you add more securities to a portfolio its variance will decrease, as the correlation is always less than or equal to 1. |

haarlemmer |
I think Philip has the point |

kulla |
I need not to be true .. what if my portfolio consists of stocks from the same sector like for e.g. homebuilders, then portfolio variance increases |

widearea |
kulla: even if your portfolio has securities from the same industry, its variance still decreases if you add more securities (of the same industry) in it. However, your portfolio will have some unsystematic risk associated with that industry. |

Rotigga |
I. need not be true. You can load up your portfolio with a multitude of high risk stocks and your variance will increase. |

nike |
I is generally true. Even if your portfolio has many high-risk stocks they may offset each other. Correlation is more important than individual variances. |

ljamieson |
It would be better worded that as the "level of diversification increases". If you are not diversifying as you add assets, you are really just accomodating sector risk. You may as well go all-in with the riskiest asset in a sector if you will just take one sector. |

bobert |
If you have all similar stocks from the same sector, you decrease the variance by having more than a few stocks, which is a poor, but albeit type of diversifying stocks. If you have a bunch of high risk stocks that aren't necessarily in the same sector, then they are still being offset by the others, therefore lowering variance. |

steved333 |
The only way that I is false is if you continually add stocks with either the exact same or greater variance as the portfolio. Mmmm, not really likely there, even from the same sector or asset class. They may be similar, but the more securities you have in a portfolio, the more you cut out more and more of the unsystematic risk therein. Why else would you even build a portfolio if not to try to achieve higher rewards with lower risk? |

mordja |
impossible to have identical companies thus correlation will be <1, thus diversificatin occurs. variance declines, regardless of the company added. |

johnowens |
arguing against I is crazy. read your notes before deciding that years of portfolio management theory is incorrect. adding of stocks to a portfolio ALWAYS creates diversification. |

johntan1979 |
Agree with johnowens. Try working out an example, i.e. adding more and more stocks to a portfolio and then come and argue that the portfolio variance will not decrease all the time. |

gill15 |
It doesnt always decrease portfolio variance MATHEMATICALLY. Thats the thing. If all the securities are 100% positively correlated the portfolio variance wont decrease. In reality they are not 100% but for the sake of this question, my thinking is mathematically. I got it wrong. |

gill15 |
I`m 100% right. Straight from the notes. Adding securities to a portfolio that are NOT perfectly, positively correlated with each other will reduce the standard deviation of the portfolio. |

robbiecow |
Here is the math: 50% in Stock A w/ sigma = 10% 50% in Stock B w/ sigma = 10% Both Stocks have rho = 1 (perfect correlation) 1% = (.5^2 * .1^2) + (.5^2 * .1^2) + 2 *.5 *.5 * (1 * .1 * .1) |

ascruggs92 |
I is true assuming we are adding securities with the goal of minimizing risk for a desired expected return. Considering that assumption is the basis of portfolio management theory, I will always be correct in the realm of academia (i.e. this test) |

houstcarr |
robbiecow is spot on. this LOS was all about the math involved in calculating portfolio variance. doesn't matter how many securities you add to a portfolio if all of their correlations are equal to 1 and have the same individual variances, the portfolio variance will never change. granted, in reality you'll probably never find two securities with correlation = 1 and exact same variance |

chesschh |
Dont blind yourself only looking at stocks... the market also conforms commodities and currencies and there ARE correlation exactly 1. I is incorrect |