# Reading 43: Portfolio Risk and Return (P.1)

**Calculate and interpret major return measures and describe their appropriate uses**

**Holding period return (HPR)**

**Average returns**

- The arithmetic mean return is the simple average of a series of periodic returns.
- The geometric mean return is a compound annual rate.

- The money-weighted rate of return is the internal rate of return on a portfolio based on all of its cash inflows and outflows.
- Other return measures

- Gross return: refers to the total return on a security portfolio before deducting fees for the management and administration of the investment account.
- Net return: refers to the return after these fees have been deducted.
- Pretax nominal return: return prior to paying taxes. Dividend income, interest income, short-term capital gains and long-term capital gains may be taxed at different rates.
- Real return: is nominal return adjusted for inflation.

Ex: Nominal return: 7%, inflation: 2%. ⇒ Approximately: 7-2 = 5%, real return: 1,07/1,02 = 4.9%

- A leveraged return: return to an investor that is a multiple of the return on the underlying asset.
**Equal (% of gains or losses on investment)/ cash investment.**

**2. Describe characteristics of the major asset that investors consider in forming portfolios**

- Asset classes with the greatest average returns also have the highest standard deviations (risk) of returns.
- Liquidity is an additional characteristic to consider when choosing investments because liquidity effect the price and expected return of a securities.
- US, small-cap stocks ⇒ greatest average returns & greatest risk over period. Treasury bill ⇒ lowest (return & risk).

* 3. Calculate and interpret the mean, variance and covariance (correlation) of asset returns based on historical data*.

- Variance (Standard deviation) of return for an Individual security

Where: N (n): total number period

x, the mean or expected return

Measures the extent to which 2 variables move together over time.**Covariance and correlation of returns for two securities:**

- Positive covariance ⇒ the variables (rates of return on 2 stocks) tend to move together.
- Negative covariance ⇒ 2 variables tend to move in opposite directions.
- Zero covariance ⇒ no linear relationship. Knowing 1 tells nothing about 2.
- Focus on the calculation of the covariance between 2 asset’s returns using
**Historical data.**