# How we calculate your returns

Clim8 Investment Team

13 April 2022

There are a variety of ways to calculate the performance of a portfolio, and we will focus on what are arguably the three most common methods: Simple return, time weighted return, and money weighted return.

## Simple return

Simple return is calculated by dividing your current earnings (your overall gain or loss plus bonuses and rewards minus any fees) by your net contributions (your total contributions minus your total withdrawals). It is (as hinted by its name) a very simple form of calculating return. Its equation is as follows:

Where R is return, EMV is end market value, BMV is beginning market value. An example of this is as follows:

1. James invests £100 into his stock portfolio, and does not put any new money into his account for the entire qtr.
2. At the end of the qtr, the value of James’s portfolio is £110.
3. Plugging this into our equation above:

R=(110-100)/100 = 10/100 = 0.1 = 10%

R=10%

This shows that James’s return is 10%. However, this is for a very simple case. What happens if James deposits £100 on the first day of the quarter, and then the next day deposits £10 every day for the rest of the quarter? Assuming there are 90 days in a quarter, James deposits £890 over the course of the quarter (89*10+100). The end market value of James’s portfolio is £1200. Plugging this into the above formula, we get the following:

R=(1200-100)/100 = 1100/100 = 11 = 1100%

R=1100%

This is not the true return figure of James’s portfolio, and this shows how easily the return figure can be distorted by cash flows. If only there was a way to calculate the return in a way that accounted for cash flows…

## Time weighted return

It’s called a time weighted return (or TWR for short). A time weighted return can be defined as a method of return calculation that eliminates the impact of the timing of cash flows and leaves only the effects of the market and the actions of the portfolio manager. In order to calculate TWR, the performance period is broken down into sub-periods. The returns of the sub-periods are then calculated and then geometrically linked to derive the TWR for the performance period. The formula for TWR can be seen below:

Where

TWR is Time weighted return, RN is sub period return, CF is cash flow, and EMV and BMV are the same as before.

If we take the example of James depositing £10 every day after the day he initially deposits £100, and the end market value is £1200, then the time weighted return of his portfolio is ~21.2% – a far more appropriate figure than the 1100% figure stated previously.

In fact, if we remove the market effects, and have the end market value figure be £990, (and therefore just the sum of the deposits) then the TWR is 0%. However, this method of return calculation is far from perfect because it does not account for the timing of deposits. This is important, because while many investors will hold the same stock, the timing for the investment might be different and some investors may buy more units of a security when the price of the security is low, while others may buy more units of the same security when the price is high. Thankfully, there is a form of return calculation that takes this into account; the money weighted rate of return.

## Money weighted return

As mentioned above, money weighted return takes into account both the amount and timing of cash flows into one’s investment portfolio. In simple terms, the money weighted rate of return tells you what return you’ve seen on your investments by looking at when and how much you have invested overall. One way to calculate the money weighted return is by using a formula called ‘Modified Dietz Formula’. This formula is a follows;

Where EMV, BMV, CF all remain the same as above, and Wi is weight to be applied to the cash flow on day i, and CFi is the cash flow on day i.

Lets again use James’s finances as an example, and use a 90 day quarter as a time frame. He starts off the quarter by depositing £100 in his investment account, and then deposits £10 every day for the rest of the quarter. At the end of the quarter, the value of his portfolio is £1200, and the Money weighted return is ~17.2%.

## Conclusion

There is no right method of return calculation. All methods tell a story and contain valuable information. At Clim8, we generally use a time weighted rate of return. We have no control over the size or timing of the cash flows into accounts; that power lies with our customers. As time weighted return is the return calculated independently of cash flows, we feel this method is the most suitable for our usage.