This article is to compare and summarize the differences between “Money-weighted rate of return” and “Time-weighted rate of return”. Please refer to the videos for the basics.

From the videos, the money-weighted rate of return is 12.7% while that of time-weighted is 15%. Which one more accurate? Which one should be used?

Generally, time-weighted rate of return should be used. This is because it measures the growth rate of money in each period and then takes the average (geometric mean). So, this is a measure of the real ability of a portfolio manager to grow every $1 (and not affected by the client’s decision to draw or invest money).

Then why money-weight would give a lower rate of return? This is because it calculates IRR and there is a large cash inflow right before the 2^nd period (which has a lower performance). You may think in this way: Calculating IRR is just to discount all the cash flows so that their sum has zero net present value (NPV). If the future cash flow has large value, you will get a large IRR because you need larger IRR to discount. And, similarly, if it has small value, you will get a small IRR.

Let’s exam this example. If the cash inflow at the beginning of the 2^nd period is +$100 and two years later there is an outflow of the money grown from this $100, we have the following table:

You can see that the better the performance the 2^nd period is (i.e. the larger the differences between the beginning and ending of 2^nd period is), the larger is the IRR needed to discount the cash flows so that the NPV is zero. Therefore, in our example, we have cash inflow at the beginning of the 2^nd period ($60 to buy a new stock) and the 2^nd period has worse performance than the first period, the IRR comes out to be less than the time-weighted method.

So,

Finally, if a manager has complete control over the cash flows, then it is more appropriate to use money-weighted rate of return. This is because it is the manager’s decision to make all those cash flows (not the clients), so this action should also be taken to measure the ability of the manager. Money-weighted rate of return is, thus, a better measurement.