It might seem like an easy and obvious case, given the recent bear market and subsequent recovery, but let’s take a look at the true numbers.

I’m going to use both Time-weighted Return (TWR) and Money Weighted Return (MWR). This will help make it clear whether my decision to add the use of margin (i.e., buy shares by borrowing money), and the following deposits were a positive move or not.

Before I continue, I want to state I know that the Corona-crisis is still ongoing. Governments have only recently started to look at exit strategies or only executed the first steps to reopening after a lockdown. Still, since I topped up my account and am no longer in red, I think it’s an excellent time to drill into the returns.

The time-weighted rate of return, also known as the geometric mean of return, measures the return of each intermediate interval and aggregates it to generate the return of the entire period. Intermediate cash inflows or outflows do not impact this rate. The growth in each period is multiplied to arrive at the rate of return for the actual period.

Sounds complicated so let us use numbers. Assume that we want to determine the 1-year return of the following cash flows:

**Time (in months)** | **Initial Value** | **Deposit/withdraw** | **Final Value** |

0 | 100 EUR | 0 | |

6 | 110 EUR | 10 EUR | 100 EUR |

12 | 120 EUR | 0 EUR | 120 EUR |

The final value is the initial value adjusted for any deposits or withdrawals. Since there is a withdrawal in our case, the final value is lesser than the original portfolio value after 6 months.

If we ignore the impact of the intermediate cash flows and holding period returns, the 1-year return would simply be 120/100 – 1 = 20%

However, there has been a withdrawal of 10 EUR that needs to be accounted for.

TWR is given as:

(1+*HPR1*)* (1+*HPR*2)*……… ( (1+*HPR*n) – 1

Here *HPR* stands for holding period return. In our case, there are two periods: 0-6 and 6-12. Therefore,

TWR = (1+10%)*(1+20%) – 1 = 32%

By breaking the 1 year into two sub-periods, TWR ensures that the timing of inflows or outflows does not impact the return.

The result would have been the same had the 10 EUR withdrawal been at the end of 3 months with the value at that time being 110 EUR.

I think from the examples above, you can see when there would be good or bad times to use TWR to measure how your portfolio has done.

A small portfolio with 10,000 EUR that excelled over 1 year and doubled up to 20,000 EUR at the end of that year, made a great return. If you then deposited 200,000 EUR and lost 50% in the following year, you would have a crippling loss of 110,000 EUR in the final year. However, your TWR is a 0% return – that is a bad TWR and not representative of your portfolio gain or loss.

If there are consistently small additions and subtractions from the portfolio is when you will have a “good” TWR because it more accurately represents the portfolio positioning. Large deposits and withdrawals can easily turn a “good” TWR into a “bad” TWR.

Money weighted return or the Internal Rate of Return is the rate of return that makes the present value of all future cash flows equal to the initial cash outlay. Using the same numbers from earlier, MRR can be calculated as:

100 = 10/(1+MWR) +120/(1+MWR)2

Or MWR = 14.66% (use Trial and error or goal seek option in Excel). Now, this is the 6-month return. The 1-year rate would be 1.14662 – 1 or 31.47%

Since there was a withdrawal just before the time when the growth was higher, MWR had a lower rate when compared to TWR.

Thx for doing such a detailed post on this. It is good to understand these concepts

THx Amber Tree. I had this in mind for a while now but it wasn’t easy to get it in writing. I found it interesting to see how TWR and MWR correlate and how it evolved during different time frames. I recommend you look at it in detail if you are interested in learning a bit about your portfolio’s performance.