# TRUE OR FALSE: As the number of assets in a portfolio increases,the variance tends towards the average s.d of the assets

## What happens when number of assets in portfolio increases?

As the number of assets in the portfolio grows, **the terms in the formula for variance increase exponentially**. For example, a three-asset portfolio has six terms in the variance calculation, while a five-asset portfolio has 15.

## What does the variance of a portfolio depend on?

By definition, the variance of a portfolio’s return is the expected value of the squared deviation of the actual return from the portfolio’s expected return. It depends, in turn, on **the possible asset returns (R), the probability distribution across states of the world (p) and the portfolio’s composition (x)**.

## What is the variance of a portfolio?

Portfolio variance is **a measure of the dispersion of returns of a portfolio**. It is the aggregate of the actual returns of a given portfolio over a set period of time. Portfolio variance is calculated using the standard deviation of each security in the portfolio and the correlation between securities in the portfolio.

## What is the relationship of the portfolio standard deviation?

Portfolio Standard Deviation is calculated based on the standard deviation of returns of each asset in the portfolio, the proportion of each asset in the overall portfolio i.e., their respective weights in the total portfolio, and also the correlation between each pair of assets in the portfolio.

## What happens to the standard deviation of return for a portfolio if we increase the number of securities in the portfolio?

As the number of securities added to a portfolio increases, the standard deviation of the portfolio becomes **smaller and smaller**.

## What is the impact of increasing the number of stocks in the portfolio?

As the number of stocks in your portfolio increases, **the overall returns on your entire portfolio usually decreases**. This is because some stocks in the stock market usually out-perform the others while most stocks give an average return.

## What does standard deviation mean in a portfolio?

The standard deviation of a portfolio **measures how much the investment returns deviate from the mean of the probability distribution of investments**. Put simply, it tells investors how much the investment will deviate from its expected return.

## Is variance the same as standard deviation?

**Variance is the average squared deviations from the mean, while standard deviation is the square root of this number**. Both measures reflect variability in a distribution, but their units differ: Standard deviation is expressed in the same units as the original values (e.g., minutes or meters).

## How do you find the variance of two asset portfolios?

**Expected Variance for a Two Asset Portfolio**

- Example.
- Expected Returns = 0.40*0.12 + 0.60*0.20 = 16.8%
- Variance = (0.40)2(0.20) 2 + (0.60) 2 (0.30) 2 + 2(0.40)(0.60)(0.25)(0.20)(0.30)
- Standard deviation = Sqrt(0.046) = 0.2145 or 21.45%

## What is the impact on the variance of a two asset portfolio if the covariance between the two securities is negative?

What is the impact on the variance of a two-asset portfolio if the covariance between the two securities is negative? **less than +1**.

## How does the correlation between returns on a project and returns on the firm’s other assets affect the project’s risk?

How does the correlation between returns on a project and returns on the firm’s other assets affect the project’s risk? **The individual projects risk may have little impact on stockholder’s risk**, viewing it in context of entire company.

## What happens to the risk of a portfolio as the number of assets in the portfolio is increased?

Diversification: generally, as the number of assets in a portfolio increases, **the risk of the portfolio decreases**. Diversification relies on a loose relationship between the returns of the assets in the portfolio.

## What increases portfolio risk?

As **the number of assets in a portfolio increases**, the correlation among asset risks becomes a more important determinate of portfolio risk. Combining assets with low correlations reduces portfolio risk.

## What does portfolio risk depend on?

Portfolio risk depends on: **Risk of individual assets.** **Weight of each asset.** **Covariance or correlation between the assets**.