on the portfolio minus the cumulative return on the benchmark

which gives us the 6.18%.

Now, clearly neither the arithmetic average, nor

the geometric average difference gave us this result, right?

What's going on here?

Why?

So to see this, again think about what we're trying to do.

We're trying to evaluate how our active portfolio value at the end of the period,

compares with the value that would have been earned with the benchmark portfolio.

Right.

So in order to make this comparison,

it's the ratio of these values that we should use.

And this would give us what?

The ending value of our portfolio is 97.99,

the ending value for the benchmark portfolio is 104.17.

So what is the monthly excess return over the three month period?

So what is the per month excess return?

So I'm going to take the 1 over 3rd root of that minus 1,

well, that gives me -2.02%.

This is the monthly excess return.

Right?

So -2.02%, monthly excess return over the benchmark.

Right? So now given this value,

we can compute the cumulative excess return over three months.

All right.

What is that?

1- 0.0202 compounded for

three months- 1, which gives us -5.94%.

So this is the cumulative excess return, all right?

Based on the end of period portfolio values, right?

So think about what this cumulative excess return means, right?

This is a loss of $5.94, right?

On $100 right,

per $100 of ending value of the benchmark portfolio, right?

So the benchmark portfolio ended up at 104.17

x (-0.0594) which gives us exactly

the $6.18 that we were looking for before.

And this is exactly equal to the difference

in our portfolio ending value and the benchmark ending value.