## Thursday, October 3, 2013

### Fast Calculation of Internal Rate of Return (in Multiple Choice Situations...), Part II

In my last post, I covered a "fast" way to solve multiple choice internal rate of return exercises.  In today's post, I look at a second quick method.

Recall the details from the last post:
• Account market value on 3/31 is \$56.3 million
• Account market value on 4/11 is \$58.2 million (prior to contribution on same day)
• Contribution of \$9.8 million is made on 4/11
• Account market value of \$69.6 million on 4/30
Given the above, is the monthly internal rate of return closest to:
a)  9.3%, or
b) 2.7%, or
c) 5.6 ?

The second fast method involves use of the Modified Dietz formula.  Modified Dietz is, in fact, a money-weighted return.  It exhibits the following traits of money-weighted returns:

• the portfolio is valued only at the start and end of the period
• interim external cash flows are day-weighted within the evaluation period
In fact, Modified Dietz gives a first-order approximation to the internal rate of return.   (One missing element is the time value of money.)  Plus, if you are like most people, you probably think calculating Modified Dietz returns is easier than calculating internal rate of return!

Recall the formula for Modified Dietz is:

Plugging our data into this formula, we get the following:

From this it is clear that the answer is option c), the return of 5.6%.  That wasn't painful at all!  This method may be even faster than the last method!

Modified Dietz as an approximation to IRR should work fine for fairly short evaluation periods and non-extreme cash flows.

Hope this helps!

P.S. #1:  Modified Dietz can, of course, be used to calculate sub-period returns, which we then geometrically link to get the time-weighted return.  Recall the following traits of the time-weighted return:

• revaluation on a frequent basis (rather than just simply at the start and end of the period)
• if valuations are done on external cash flow dates, the geometrically linked return is the so-called "true time-weighted return"
• if valuations are done frequently but not on the cash flow dates, then the geometrically linked return is an estimate of the time-weighted return
P.S. #2:  The picture above is Michael Phelps, considered to be the fastest person in water. I figured I'd use him today, since we used the fastest person on land (Usain Bolt) yesterday.

Happy studying!