# Performance metrics

So far, we have discovered the core asset classes and a variety of investment options. Throughout the course, we have seen topics and examples that talk about performance and returns, gains and losses. Now, it is time to clarify what all that means and to see how to measure your investment performance.

### What does investment performance mean?

In the investments world, performance is essentially translated to returns (gains or losses) on your investment and the progress of those returns over time.

**Ok then, let’s start by understanding what your investment return is:**

In finance, your return is the money you made (gains/profits) or lost (losses) on your investments over a specific period of time. It is the change of value of your investment over time and it can be expressed in money terms or in percentage terms.

## Rate of return

How do you know if your investments did well or not? There are multiple ways to measure the success of an investment, but one of the main ones is the rate at which the investment’s value has grown during a certain period. We call **holding-period return** (HPR) the rate of return over the lifetime of your investment, from purchase to the present or to the time it was sold. This depends on the total increase (or decrease) in the value of your investment including any dividends or extra income. We define the **rate of return** as the amount earned over a specific timeframe per dollar invested (in the initial purchase). The HPR formula is really simple and self-explanatory:

HPR = (Ending value + Dividends – Begining value) / Beginning value

Here is a real-world example to see how HPR works:

You bought 1 Microsoft stock at the beginning of 2019 and sold it at the end of the same year (holing period of 1 year), and you want to figure out how well your investment did:

- Microsoft stock price on 1/1/2019: $100.00
- Microsoft stock price on 12/31/2019: $155.00
- 2019 dividend payment: $1.90

HPR = ($155 ending value + $1.90 dividend – $100 beginning value) / $100 beginning value = 0.57, or 57%

The holding-period return is a really simple, yet powerful tool to assess your investment’s performance over a single, specific timeframe. However, investors typically are interested in knowing more about their investment’s performance in certain circumstances. For instance, imagine you started investing with those $100 on a Microsoft stock but you added funds to your investments every year, say $100 every year. Now, this got a bit more complicated and the HPR may not tell us the whole story. Let’s see what tools we can use to get a full picture of our investment’s performance:

#### Arithmetic average

This is the typical average we are all used to. It is calculated by summing all the value at every period (e.g. value of an investment at the end of every month) and dividing that by the number of periods of the investment.

For instance, if we wanted to measure the arithmetic average of the yearly returns from your Microsoft investment over the past 5 years (from 2015 to 2019), we would do the following:

**Record**the value of the asset at the end of every month from the start:- 2015: $50
- 2016: $58
- 2017: $82
- 2018: $100
- 2019: $155

- Compute every month’s
**holding-period return**:- 2015: 39%
- 2016: 16%
- 2017: 41%
- 2018: 22%
- 2019: 57%

**Sum**all of the period returns up:- 39% + 16% + 41% + 22% + 57% = 175%

**Divide**the sum by the number of periods:- 175% / 5 years =
**35% average annual return**

- 175% / 5 years =

Because this measure ignores compounding, it is not an ideal representation of a single year’s return. However, if we have no more information, it can be used as a proxy for the expected annual return.

#### Geometric average

The geometric average (also called compounded annual growth rate, CAGR, or the time-weighted average return) is a more accurate metric when trying to calculate the average compounded return in a timeframe with multiple periods since it focuses only on the returns, and not on the dollar amounts.

We calculate this measure by compounding (multiplying) the period-by-period returns and then we find the single period return that would compound to the same final cumulative return.

If we follow the previous example, we will see this measure much more clearly:

We had computed the annual returns for 1 Microsoft stock, below are the steps we have to follow to get the geometric average:

**Add**1 to each of the period’s return and**multiply**them all together:- (1+39%) x (1+16%) x (1+41%) x (1+22%) x (1+57%) = 4.3547

- Take the
*n-th*root of the above result,*n*being the number of periods in the timeframe analyzed (or the 1/*n*power):- 4.3547 ^ (1/5 years) =
**34.20% geometric average return**

- 4.3547 ^ (1/5 years) =

We also call this a time-weighted average return because it ignores the dollar amount invested and it focuses strictly on the returns. We recommend using this measure as it becomes more and more valuable over time. Also, this is the way to calculate your true return if you are reinvesting your dividends or adding funds to your portfolio periodically.

#### Money-Weighted Return

This measure is used to calculate the rate of return taking into account the varying amounts of money in a portfolio or a fund over a period of time. The money-weighted rate of return takes into account the size and timing of cash flows, so it is an effective measure for returns on most portfolios. For instance, if you add funds to your portfolio periodically, or you reinvest your dividends, it will incorporate those amounts as inflows of cash into the calculation of the rate of return. This formula is fairly complex and we don’t need to know it since the result can be easily be computed online or on a calculator.

## Historical performance

Analyzing historical (past) data can help us get an idea of what to expect for the future. Looking at how an asset performed over a period of time tells us how it reacted to the economic conditions in that period, which may help us forecast how it may perform in case those conditions are ever repeated.

#### Cumulative returns

In order to analyze an asset’s historical cumulative performance, we have to first set a specific timeframe (e.g. 5 years ago up to yesterday, or year-to-date, which ranges from the start of the current year up to today). Then, we have to specify the frequency in which the returns will be recorded. Next, we set the timeframe’s initial value as the base for calculating the subsequent returns in the frequency we chose (it could be daily, monthly, yearly, etc.). Lastly, we calculate the cumulative return for every period in that timeframe (starting from the initial value).

Let’s see an example to clarify this:

**Timeframe:**1 year**Frequency:**monthly**Initial value:**$100

The above lists the value of our investment at the end of every period (month) in our timeframe (1 year), starting with January as our initial investment value of $100. The return is calculated using January’s value and every month’s end value (e.g. May’s return = ($102 – $100) / $100 = 2%).

The graph represents the progress of the asset’s returns over the full year and it is helpful to identify trends or behaviors. Also, it is important to take into account the end cumulative return when comparing assets’ historical performance. That is the total return at the end of the timeframe analyzed, as this will tell us which assets performed the best (this is not a great measure on its own because it doesn’t take risk into account).

In our analysis, we use this method to compare different assets’ performance over various timeframes to identify possible long-term and short-term winners, as assets may behave differently under certain economic conditions.

Above is an example of a real, interactive graph used to compare the performance of all assets in one of our portfolios. We analyze daily cumulative performance over four different timeframes to identify long and short-term trends.

#### Period-over-period performance

Looking at the period-over-period performance of an investment can also be helpful to detect longer-term trends. It is calculated similarly to the cumulative performance; however, in this case, we do not use the initial value as the base for the returns, we look at each period individually and compute the percentage change from the start to the end of the period.

In the below chart, we used the same data as the cumulative performance chart; however, we plotted the monthly returns individually. This helps us focus on period-over-period behavior, which allows us to compare the present performance of an asset in a given timeframe (e.g. month-over-month, year-over-year, etc.) with its past performance in the same timeframes.

In the above example, we can see the month-over-month returns on investment. This can be a powerful tool to identify seasonal trends and possible investment opportunities.

Above is an example of a real, interactive chart we use in our analysis to compare the year-over-year (YoY) performance of various assets in a portfolio. As we can see, the period-over-period analysis can also help us identify asset correlation trends overtime.

In the next section, we will revisit and expand on the most important topic: risk. We will find out the best tools we have to identify and measure investment risks.