Calculate Compounded Returns Using Scan

Question

A portfolio starts with a value of 100.

The portfolio then experiences the following daily returns:

returns:0.01 -0.02 0.03 -0.01

where:

Each day's return should be applied to the portfolio value produced by the previous day.

Calculate the portfolio value after each daily return is applied.

Expected result:

101 98.98 101.9494 100.9299

Solution

{x*(1+y)}\[100;returns]

Alternative Solution

100*prds 1+returns

1+returns turns each return into a growth factor (1.01 0.98 1.03 0.99), prds takes the running product of those factors, and multiplying by 100 scales them to the starting value.

Explanation

The scan iterator:

\

returns every intermediate result.

The function:

{x*(1+y)}

takes:

• x as the current portfolio value
• y as the next daily return

For each iteration, the portfolio value is updated using:

newValue = currentValue * (1 + return)

The calculation proceeds as follows:

Day 1: +1%

100*(1+0.01)

Result:

101

Day 2: -2%

The 2% loss is applied to the new portfolio value of 101:

101*(1-0.02)

Result:

98.98

Day 3: +3%

98.98*(1+0.03)

Result:

101.9494

Day 4: -1%

101.9494*(1-0.01)

Result:

100.9299

(q displays floats to 7 significant digits by default; the full value is 100.929906. Use \P 10 to show more digits.)

The scan expression:

{x*(1+y)}\[100;returns]

returns every intermediate portfolio value:

101 98.98 101.9494 100.9299

This is useful when modelling:

• Cumulative portfolio value
• Compounded returns
• Growth of capital over time
• Running NAV

Unlike a simple sum of returns, each return is applied to the current portfolio value, making this a natural example of when the scan iterator is required to carry state forward between iterations.