## Basic Portfolio Return Calcuations

Risk, return, and the relationship between the two is a vital concept in the CFA curriculum.

On the CFA Level 1 Exam there are two entire readings devoted to understanding this material.

This post covers part of the first reading and lists the basic measures of portfolio return.

## How to measure investment returns for CFA L1

Obviously as an investor or investment analyst it is imperative to be able to calculate the return of a given investment. There are several methods to do so including the holding period return, average return, and geometric mean return.

### Calculating Holding Period Return

The holding period return (HPR) is simply the percentage increase in the value of an investment over a period of time. HPR is calculated as:

We can also compound our holding period return over multiple periods to get a final return:

### Calculating Average Return

The **simple average** of a series of period returns is equal to:

### Calculating Geometric Mean Return

The **geometric mean** is usually used when we want to calculate the __average compound growth rate__ of an asset over time. Unlike the arithmetic mean it does not assume that the amount invested is the same in each period. For the CFA Level 1 exam this is a vital equation/concept to know.

Mathematically:

### Calculating the Money Weighted Rate of Return (MWRR)

The **money weighted rate of return (MWRR),** or dollar-weighted return, is the IRR on all funds invested during a period. If you do have to calculate MWRR on the exam, enter each cash flow into your calculator and CPT the IRR.

*You are unlikely to need the equation but it is:*

MWRR takes into account the amount of money invested in each period and gives us the return for that actual invested amount. Given that it is not especially standardized, however, it is difficult to compare MWRR between different investments.

### Analyzing a Return/Calculating Portfolio Returns

We **annualize returns** to make investments of different maturities/lengths of time easier to compare:

Where N is the number of periods within a ear. So for example if we’re dealing with quarterly returns, N would equal 4.

A **portfolio return** is just the weighted average of returns on each of the individual assets. For a two asset portfolio this would be:

### Some Basic Vocab around Portfolio Returns for the CFA Level 1 Exam

In addition to the calculations listed above you always need to understand what *type *of return your calculation is yielding. Is it before or after taxes? Is it in real or nominal terms? Here's a quick summary of the differences.

#### The difference between gross and net return measures

**Gross return**is the total return before deducting any management and admin fees**Net return**is the return after all fees have been deducted. Investors usually care about net returns (the money actually going into your pocket)

#### Pre and Post Tax Returns

**Pretax nominal return**is the return before paying taxes**After-tax nominal return**is the return after paying taxes. Again this is the return most investors care about.

#### Real, Nominal, and Leveraged Returns

**Real return**is simply the nominal return adjusted for inflation, i.e. subtract inflation- By adjusting for inflation the real return is more useful for comparing international investments or investments over different time horizons

**Leveraged return**is the gain or loss on investment as a % of the cash invested. As we’ve previously covered, leverage can increase returns but also magnify losses.