**This is Part 3 of a Series.**Go to Part 2:

**Time-Weighted Rate of Return: It's All About Relative, Simple Yields**

**Note:**

*The following is a letter addressing my partners which clarifies the money-weighted (MW) and time-weighted (TW) measures of performance. I would recommend that you read first the earlier letter before proceeding.*

March 6, 2011

TO MY PARTNERS:

Essentially, TW captures this scenario: had I started the fund with a pioneer partner in 2008 and that partner did not make any deposits to and withdrawals from the fund, he should be earning a 17.15% compounded annually. In reality, however, this may often not be the case: he may be making additions or withdrawals (these can dramatically magnify his profits or losses depending on how the fund performed after the additions/withdrawals)—this is the essence of the MW approach; it captures and weighs the timing and money amounts committed for any given period and pinpoints the real absolute returns per actual fund results.

For my case, my total invested cash (which were infused in varying amounts at different time periods) yielded an actual net, money-weighted 42.79% internal rate of return. TW would be more useful in a scenario where the fund manager cannot control his investors' deposits or withdrawals. MW would be more appropriate in the case of a private individual or a private organization wherein deposits/withdrawals are controlled or are subject to the manager's consent/decision.

There maybe times when MW is negative and TW is positive (and vice versa). Consider this example:

**Year 1**

Deposit (withdrawal) = 1

Beginning equity value = 1

Net gain (loss) = 2

Ending equity value = 3

Rate of return = 200.00%

**Year 2**

Deposit (withdrawal) = 20

Beginning equity value = 23

Net gain (loss) = (15)

Ending equity value = 8

Rate of return = -65.22%

**Year 3**

Deposit (withdrawal) = 0

Beginning equity value = 8

Net gain (loss) = 10

Ending equity value = 18

Rate of return = 125%

The time-weighted return for this example should be 32.91% computed by first getting the effective simple percentage gain for the whole 3-year period:

(1+200%) x (1-65.22%) x (1+125%) - 1 = 134.78%

The 134.78% simple return is annualized as follows:

1 x (1+134.78%) = 2.35

(2.35/1)^(1/3)-1 = 32.91%

Thus, the portfolio yielded a 32.91% time-weighted return. Caution though, since this may somewhat be deceiving. Commonsense dictates that the fund manager's total investment of Php21.00 (a peso in year 0 and 20 pesos in year 2) ended up as Php18.00 in year 3, resulting to a net loss of Php 3.00. In absolute terms, the fund lost money.

The money-weighted approach does a better job to capture this reality, albeit harder to compute manually. Nonetheless, it can be arrived at by organizing the deposits and withdrawals into tabulated cash flows then by running an internal rate of return (IRR) iteration:

**Year 0**

Cash outflow (inflow) = (1)

Discounted cash flow = (1)

**Year 1**

Cash outflow (inflow) = 0

Discounted cash flow = 0

**Year 2**

Cash inflow (outflow) = (20)

Discounted cash flow = (26.58)

**Year 3**

Cash inflow (outflow) = 18

Discounted cash flow 27.58

*Net Present Value (NPV) = 0*

Hence, we can say that although the fund yielded a time-weighted 32.91% return (i.e. had a partner invested a certain peso amount in it since the beginning and did not make and additions or withdrawals, he should be happy with the 32.91% compound interest), in real, absolute hard cash returns, however, the fund actually lost Php3.00 with a money-weighted return (i.e. IRR) of -13.26%.

Going back to my personal portfolio’s performance, while its 3-year TW rate of return has been 17.15%, its MW return, on the other hand, has been 42.79%. Refer below for the details of my personal portfolio’s cash flows:

Additional Notes: So as to arrive at a more accurate MW rate of return, the annual durations from the start to each month period (under the “Year” column) were derived and used in the discounting of each cash flow. December 2010’s Php647,784.75 is not really a cash inflow wherein I liquidated my stock positions; it is but the actual ending equity value of my portfolio at that period presented as an inflow for IRR computation purposes. When future cash flows are discounted to its present value at the rate of the computed IRR, the net present value (NPV) or the sum of all discounted cash flows should be equal to zero.

Below chart graphically compares the achieved rates of return among my personal portfolio’s MW and TW returns and the Philippine Stock Exchange Composite Index (PSEi).

**• Personal-MW: Money-Weighted Return of Managing Partner's Personal Portfolio**

• Personal-TW: Time-Weighted Return of Managing Partner's Personal Portfolio

• PSEi: Philippine Stock Exchange Composite Index (without dividends)

• Personal-TW: Time-Weighted Return of Managing Partner's Personal Portfolio

• PSEi: Philippine Stock Exchange Composite Index (without dividends)

My personal portfolio’s MW return ending at 191.15% gain after 3 years is the equivalent of the computed 42.79% IRR. Similarly, its TW counterpart ending with a 60.76% gain is equivalent to 17.15% compounded annually; lastly, the PSEi ending at 12.93% translates to 4.14% annually.

Hope this clarifies well the subject matter. Should you have queries or clarifications on measuring performance, I’m more than willing to entertain them.

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