Time weighted and dollar weighted returns. Dollar weighted and time weighted returns are two methods of measuring performance or a rate of return on an investment portfolio, and each of these two approaches have particular instances where it's preferred or over the other. So let's dig in further and first take a look at time weighted return. Now, by definition, time weighted return is the compound rate of a growth over a stated period of $1 initially invested in the account. Well, how is that done? Well, it actually requires that you revalue the account every time there's an incoming cash inflow or cash outflow. Now, we do that because the time weighted return derives its name from the fact that each sub-period return, the periods between cash flows, receive a weight proportional to the length of the sub-period relative to the full length of the evaluation period, which means each return is weighted by the time that it was included in that evaluation period. Now, let's take a look at an example. Here we have a portfolio over three periods with various beginning and ending values and various cash flows throughout the period. From there, we calculated a period return for each of those periods, and to do that, we simply take the ending value of the period minus any cash flows, so we back out any cash flows, and divide all that by the beginning value of the period minus one. Well, what does this do? Well, it eliminates the effect of the portfolio cash flows on the returns that we're calculating, and because of that, the calculation is not sensitive to the contributions or withdrawals. And in most situations, an investment manager like a mutual fund manager, has little or no control over the size or even timing of the external cash flows, the investments or redemptions into and out of the fund. Therefore, in these circumstances, folks generally prefer a rate of return measure that is not sensitive to the cash flows if they want to evaluate manager's investment actions and how they have affected account value, and that's exactly what a time-weighted return will do for you. So going further into this example, if we then link each period return and multiply them in a compounding manner, we can calculate the time weighted return for the portfolio across the three periods. Now, despite its useful characteristics, a time-weighted return does have an important disadvantage. It requires account valuations to be done essentially every day to take in account all the cash flows in and out of the account. So it could be quite cumbersome. Now let's take a look at money weighted return. By definition, it measures a compound growth rate of all funds invested in an account over the evaluation period. You can also hear it referred to as the internal rate of return or the IRR, but in the end, the money weighted return is that discount rate that sets the present value of all cash inflows equal to the present value of all cash outflows. So because of that, unlike a time weighted return, a money weighted return does not just calculate investment performance. It also takes in to account all the cash flows coming in and out of the account. Let's take a look at an example. Here a stock was purchased for $100 and sold exactly two years later for $105. The investor also received a dividend during the period. What is the money-weighted return? So here you'll see all of the cash flows in and out for the investor throughout the period. Again, if we remember, a money-weighted return is when we calculate the discount rate where the present value of all outflows equals the present value of all inflows. You'll get to this pretty complex formula to calculate the money-weighted return. Thankfully for us, Excel has a nifty function called the IRR function, where we would capture all the cash flows to calculate a money-weighted return of 3.5%. Now, under normal conditions, a money-weighted return and a time-weighted return will produce similar results. However, when there are large external cash flows relative to the account's value and the account's performance is fluctuating significantly during the measurement period, then the money-weighted return and a time-weighted return can differ significantly. Now, the most obvious examples and when you would prefer to use a money-weighted return measure is when an investment manager does control timing in the amounts of cash flows into an account. For example, managers of various types of private equity investments or funds have arrangements that allow them to call capital from their investors, and it's usually at the manager's discretion ultimately when they will return original capital to investors and any earnings on that capital. And because of that, it's generally agreed that a money-weighted return is a more appropriate measure of account returns in those circumstances.