# Level 1 CFA® Exam:

Return and Asset Classes

There are two possible sources of return on a financial instrument. The first is income that you may earn on it, e.g. dividend on a stock, the other is a capital gain involved in a possible increase in the price of the financial instrument.

### Holding Period Return (HPR)

The simplest measure of return is the so-called holding period return (HPR), which you can analyze in this mathematical expression:

\(HPR=\frac{P_1+D_1}{P_0}-1=\frac{P_1-P_0+D_1}{P_0}=\frac{P_1 - P_0}{P_0}+\frac{D_1}{P_0}= CG+R_d\)

- \(HPR\) – holding period return
- \(P_1\) – price received at the end of the holding period
- \(D_1\) – income (e.g. dividend) paid by the investment at the end of holding period,
- \(P_0\) – initial investment
- \(CG\) – capital gain
- \(R_d\) – dividend yield

HPR is a measure used to compute return over a single period. You can use HPR to compare two investments only if they last for the same period.

### Arithmetic Return

Another type of return is the arithmetic or mean return. It is a very popular measure. It can be represented with this expression:

\(R_A = \frac{R_{1} + R_{2} + \ldots + R_{T-1} + R_{T}}{T} = \frac{1}{T} \times \Sigma^{T}_{t=1} R_{t}\)

- \(R_A\) - arithmetic return
- \(R_{t}\) - return in period "t"
- \(T\) - total number of periods

### Geometric Mean Return

An equally popular type of return is the geometric mean return, expressed as follows:

\(\overline{R}_{G} = \sqrt[T]{(1+R_{1})\times (1+R_{2})\times \ldots \times (1+R_{\text{T-1}})\times (1+R_{T})} - 1 =\\= \sqrt[T]{\prod_{t=1}^{T}(1+R_{t})} - 1\)

- \(\overline{R}_{G}\) - geometric mean return
- \(R_{t}\) - return in period "t"
- \(T\) - total number of periods

(...)

### Money-Weighted Return

To measure return on investment over multiple periods, we can also use the money-weighted return. Money-weighted return is similar to the internal rate of return. We use it when the amount of the investment changes from period to period. Money-weighted return is expressed with this formula:

\(\Sigma^{n}_{t=0}\frac{CF_{t}}{(1+IRR)^{t}}=0\)

- \(CF_{t}\) - after-tax cash flow at time "t"
- \(IRR\) - internal rate of return
- \(t\) - moment of time

### Annualized Return

As far as the computation of returns and the comparison of returns on different investments are concerned, it is important to be able to convert rates of return to a single period. The most commonly used measure is the annualized rate of return, which you can compute using the following formula in your level 1 CFA exam:

\(r_{annual} = (1+r_{period})^{c} -1\)

- \(r_{annual}\) - annualized return
- \(r_{period}\) - the return for the period
- \(c\) - number of periods in a year

### Portfolio Return

The portfolio return can be represented with this expression:

\(R_{P} = \Sigma^{N}_{i=1} w_{i}\times R_{i},\\ \Sigma^{N}_{i=1} w_{i} = 1\)

- \(R_{P}\) - portfolio return
- \(w_{i}\) - the weight of asset "i" in the portfolio
- \(R_{i}\) - the return on asset "i"
- \(N\) - number of assets in the portfolio

So, the portfolio return is a weighted average of the returns of the individual assets in the portfolio. This is very important information and we will use it when we talk more about portfolio diversification in one of the subsequent lessons on portfolio management.

### Nominal Return vs Real Return

An investor must realize that return on investment should be adjusted for inflation and must be able to distinguish between nominal return and real return. Real returns are nominal returns adjusted for inflation. Have a look at the equation:

(...)

Let’s now take a look at the characteristics of major asset classes. There are many lines along which we can divide different types of assets. However, the basic characteristics of financial assets, i.e. return and risk, allow us to identify major asset classes.

They include:

- large company stocks,
- small company stocks,
- long-term corporate bonds,
- long-term government bonds, and
- treasury bills.

Important conclusion for an investor: a higher return generally involves a higher risk

In the case of financial assets, return and risk usually adequately define an investment. Still, financial assets have other characteristics that an investor should consider, e.g. skewness and kurtosis.

Skewness is a statistical measure of the asymmetry of the observed returns. It tells us about the dispersion of results around the mean.

Kurtosis is a measure of the concentration of results. It shows us how results are concentrated around the mean.

Finally, there is one more significant aspect: the liquidity of the market for particular assets. In a consequence of low liquidity, it is more difficult to convert assets into cash, which strongly deters investors.

- In your CFA exam you should know the following return measures: holding period return, arithmetic return, geometric mean return, money-weighted return, time-weighted return, annualized return, and portfolio return.
- Real returns are nominal returns adjusted for inflation.
- Major financial asset classes include: large company stocks, small company stocks, long-term corporate bonds, long-term government bonds, and treasury bills.
- Skewness is a statistical measure of the asymmetry of the observed returns.
- Kurtosis is a measure of the concentration of results.
- In consequence of low liquidity, it is more difficult to convert assets into cash.