At Wealthsimple, we calculate your progress in three ways and each measure serves a different purpose. At the end of this FAQ, we'll use an example to illustrate how each type of performance is calculated.
Simple (Naive) Return
Simple Return is easy to understand but may not accurately reflect your true performance.
Simple Return is a basic calculation of your Net Earnings / Net Deposits. It is the easiest calculation to understand, but may not correctly reflect what has actually gone on in your account over time. This calculation takes all of your deposits and assumes they were added to your account on the first day the account was funded. The calculation can also appear incorrect if you've earned positive returns and withdraw more funds than you have deposited.
Time-Weighted Return (TWR)
TWR measures the impact of the market and skill of your portfolio manager.
TWR is a common way to check in on how your portfolio has performed over time and is a good reflection of how your portfolio manager or advisor has performed since the first day your account was funded. It ignores your deposit and withdrawal activity and only looks at how your portfolio has actually performed. It does this by carving the time since you first funded your account into different slices (a new slice starts each time funds are added or withdrawn from the account) and these are linked to show you your overall performance.
Money-Weighted Return (MWR)
MWR measures the impact of the market, the skill of your portfolio manager and the influence of your deposit/withdrawal activity on the value of your portfolio.
MWR determines how you got to the current value of your portfolio assuming that all of your deposits earned the exact same rate of return. This type of return is influenced heavily by the timing and amount of money moving in and out of your account. If you make a large deposit and the market goes up, it will influence your MWR upwards (and vice-versa).
You decide to fund your Wealthsimple account with $1,000 on January 1st. The first 364 days of the year are great and your portfolio earns $100. You decide to add another $100,000 on December 31st and over that one day your portfolio loses a total of $101. What are your returns?
Deposit 1: $1,000
Deposit 2: $100,000
Net Deposits: $101,000
End Portfolio Value: $100,999
Net Earnings: -$1
Performance in Time Slice 1: 10%
Length of Time Slice 1: 364 days
Performance in Time Slice 2: -0.0009%
Length of Time Slice 2: 1 day
What is your Simple Return?
Simple Return = Net Earnings / Net Deposits
Simple Return = -$1 / $101,000
Simple Return = -0.00099%
What is your Time-Weighted Return?
TWR = Performance in each time slice weighted by the length of each time slice.
TWR = [((1+(.10))^(364/365)) * ((1+(-(0.000009)))^(1/365))] - 1
TWR = 9.97%
What is your Money-Weighted Return?
MWR = -0.07865%
MWR is verified by applying the same rate of return to both cash flows and ensuring this adds up to End Portfolio Value.
$100,999 = ($1,000 * (1+(-0.0007865))) + ($100,000 * (1+(-0.0007865))^(1/365))
$100,999 = $100,999
Here we see an example where your earnings are negative even though your TWR is positive. Although confusing, fundamentally this makes sense.
From the first day of funding, the assets selected and held in your portfolio have increased in value (measured by TWR). Your earnings are negative as a result of your $100,000 deposit occurring before a day of negative performance.