When you invest with a Roboadvisor, they usually display your investment returns in your dashboard or in your performance summary page.

You may have come across the term ‘simple returns’.

Here are some examples:

Simple returns basically shows how much profit you made with your investment.

Formula: Net gains / Total invested amount X 100%

So, if you had invested $1,000 in January and your portfolio at the end of Dec is valued at $1,200. You have made $200. Your simple return would be $200/$1000 = 20%

But sometimes, the dashboard may show a time-weighted return or money-weighted return and the value may be drastically different from your simple returns.

For example:

So which metric should I, the average investor, use?

Why are they so different?

TL;DR: Simple returns are more meaningful for typical investors; time-weighted returns are used to measure the portfolio returns ignoring the effect of cash flows in and out of the portfolio.

Let me illustrate the different returns with a hypothetical scenario.

## Three Hypothetical Investors

Let’s imagine that an imaginary Roboadvisor offered a new portfolio X in 2020.

The portfolio was valued at $1 at the beginning of the year. And shortly after the COVID19 pandemic hit the world, the portfolio dropped in price to $0.50 in March. And at the end of the year, the portfolio increased to $1.50.

There were three hypothetical investors who invested in this portfolio:

- Mr Fearful – he panicked and sold half of his portfolio when the price dropped.
- Mr Brave – he contributed more when the price dropped.
- Mr. Buy-and-hold – he just held his portfolio and never made any contributions or withdrawals

### Mr Fearful’ Simple Return

Mr Fearful invested $500 initially into portfolio X. He bought 500 units for $1 each.

However, when the price dropped to $0.50 in March, he got afraid and sold 250 units for $0.50 each for a total of $125.

He held the remaining 250 units and the value grew to $375 ($1.50 x 250 units) by the end of the year.

So for the year 2020, his total invested amount is $500 – $125 (the amount he withdrew in Mar) = $375.

His portfolio at the end of the year is $375.

For him, his net gain is zero because he invested $375 and had $375 at the end of the year.

His simple return is 0/375 = 0%

### Mr Brave’s Simple Return

Mr Brave also invested $500 initially into portfolio X for the price of $1 for each unit.

When the price dropped to $0.50, he listened to his financial advisor and contributed another $250 to buy another 500 units of portfolio X. Now he has a total of 1,000 units (500 bought in March and 500 initially bought in Jan).

By the end of the year, his portfolio increased to $1,500 ($1.50 x 1000 units).

His net profits would be $1,500 – $500 – $250 = $750

His simple return is 750/750 = 100%

He patted himself on the back because he actually doubled his investment during the year of the pandemic.

### Mr Buy-and-hold’s Simple Return

Mr Buy-and-hold invested $500 into his portfolio in Jan and bought 500 units for $1 each.

He simply hold on to it even when the value of his portfolio dropped in March and never made any new contributions or withdraw any amount.

At the end of the year, his portfolio value grew to $750 ( $1.50 x 500 units). His net gain is $750 – $500 = $250

His simple return would be $250/$500 = 50%

Profits | Simple Return | |
---|---|---|

Mr Fearful | 0 | 0% |

Mr Brave | $750 | 100% |

Mr Buy-and-hold | $250 | 50% |

## Time-Weighted Return

The time weighted return is basically the multiplication of the rate of returns over sub-periods which results in the total return of the overall period.

The formula is given as:

This method of calculation removes external cash flows from the calculation of the return. Cash flows can be withdrawals, deposits or fees.

What do I mean by that? Let us look at the three hypothetical investors. Let us start with Mr Fearful

### Mr Fearful’s Time-Weighted Return

Here are Mr Fearful’s portfolio values and cash flows

Month | Portfolio Value | Cash flow |
---|---|---|

Jan | $500 | $0 |

Mar | $250 | -$125 |

Dec | $375 | $0 |

For the first sub-period (Jan-Mar), Mr Fearful’s Holding Period Return (HPR_{1}) is $250/$500 – 1 = -0.5 = -50%

For the second sub-period (Mar- Dec), with a cash flow of -$125, Mr Fearful’s Holding Period Return (HPR_{2}) is $375/($250 + -$125) – 1 = 2 = 200%

The total Time Weighted Return (TWR) is (1+HPR_{1}) x (1+HPR_{2}) – 1 = (1+ (-0.5)) X (1+2) – 1= 0.5 = 50%

Mr Fearful’s time weighted return is %50.

### Mr Brave’s Time-Weighted Return

Here are Mr Brave’s portfolio values and cash flows

Month | Portfolio Value | Cash flow |
---|---|---|

Jan | $500 | $0 |

Mar | $250 | +$250 |

Dec | $1500 | $0 |

Using the same methods:

HPR1 = ($250/$500 – 1) = – 0.5

HPR2 = ($1,500 / ($250 + $250) – 1) = 2

TWR = (1+-0.5) x (1+2) = 0.5 = 50%

### Mr Buy-and-hold’s Time-Weighted Return

Here are Mr Brave’s portfolio values and cash flows

Month | Portfolio Value | Cash flow |
---|---|---|

Jan | $500 | $0 |

Mar | $250 | $0 |

Dec | $750 | $0 |

Actually, if there are no cash flows, the time-weighted return just equals the simple returns. This is illustrated with Mr Buy-and-hold.

If I use the same formula, the values are the same:

- HPR1 = ($250/$500 – 1) = -0.5
- HPR2 = ($750/$250 – 1) = 2

The time-weighted return is 50%, exactly the same as the simple return.

## Simple Return and Time-Weighted Returns For All Three Hypothetical Investors

Investor | Profits | Simple Return | Time-weighted Return |
---|---|---|---|

Mr Fearful | 0 | 0% | 50% |

Mr Brave | $750 | 100% | 50% |

Mr Buy-and-hold | $250 | 50% | 50% |

## Different Calculation Methods For Different Reasons

For the average investor, simple returns are a good enough to tell us how much money we made from how much money we had invested.

For the case of Mr Fearful, because of his ill-timed decision of withdrawing when the portfolio is going down, his net gains are zero at the end of the year.

For the case of Mr Brave, he took a risk and his contribution ended up doubling his invested amount.

A time-weighted return of 50% would mean nothing much to Mr Fearful other than remind him not to panic sell in the future.

## Time-weighted Returns is the Standard for Comparing Performance Between Different Portfolios and Funds.

The time-weighted return, on the other hand, tells us the performance of the fund itself – how skilfull (or lucky) is the fund manager.

The time-weighted return calculation removes the external contributions and withdraws to the fund – because withdrawals and deposits do affect the performance of the fund (as shown by the simple return calculation)

If you would have held on to the fund for the entire year, like Mr Buy-and-hold, you would have gained 50% at the end of the year.

So, if you want to compare portfolio X with portfolio Y, you should use time-weighted return to see how both performed.

## In Summary

The simple return method is a simple and useful method for investors to know how much they have made. It is actually the simplest type of money-weighted return calculation.

The time-weighted method accounts for cash flows and corrects it – resulting in a more accurate measurement of the performance of the portfolio itself. It is used as a standard to compare the performance between different funds and portfolios.

Modified dietz rate of return is another method which takes the weighted cash flows and is considered a more accurate reflection of an individuals rate of return. It will be another topic.

If you are a DIY investor and looking to measure how your own portfolio compares with others, you should use the time-weighted method to measure your portfolio returns. You can refer to this guide to set up spreadsheets to calculate those values (It also shows how to calculate the modified dietz rate of return).

If you are someone who just cares how much they make, then stick to simple returns and make your life simpler.

is using XIRR the same time as time weighted?