"What was my portfolio return over the last two years?" Seems like a reasonable question; unfortunately the answer is not necessarily so obvious. Consider the simple answer you would get from all too many investors.
Simple Average
"Well, last year I invested $100,000, and I lost 20%. This year I'm ahead 40%, so that's a return of 20%. So my portfolio ought to be worth $120,000, right?" Wrong. Although it sounds reasonable, consider the actual dollars.
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| Row 0 - Cell 0 | Return in year 1 | -20% |
| Row 1 - Cell 0 | Investment at the end of year 1 | $80,000 |
| Row 2 - Cell 0 | Return in year 2 | 40% |
| Row 3 - Cell 0 | Investment at the end of year 2 | $112,000 |
This type of miscalculation is no reflection on an investor's IQ but rather involves an all-too-human misunderstanding of investment math. For example, after the dot-com market crash in 2000-2002, a client of mine, a retired surgeon with a sophisticated knowledge of investing, came into my office practically in tears. He said, "Harold, last year I had an 80% return on my portfolio. This year I lost 60%. By my reckoning, I should still be 20% ahead. But I just got my statement, and it shows I'm way underwater."
Let's consider the same calculation as above.
| Row 0 - Cell 0 | Return in year 1 | 80% |
| Row 1 - Cell 0 | Investment at the end of year 1 | $1,800,000 |
| Row 2 - Cell 0 | Return in year 2 | -60% |
| Row 3 - Cell 0 | Investment at the end of year 2 | $720,000 |
Yes, a loss of $280,000 against his original $1 million investment! To break even in year 2, my client would have needed a return of almost 140% in the first year.
The math highlights the fact that significant losses require extraordinary subsequent returns in order to simply break even -- a reality to keep in mind when considering an investment in a very volatile risky position.
Internal Rate of Return and Time-Weighted Return
If the simple calculation won't suffice, let's look at using compounded returns. The most common compound return calculation is called the Internal Rate of Return or IRR. This calculation takes into account the timing of investments into and withdrawals out of the portfolio. The result is an annualized return percentage reflecting the investor's actual experience.
For example, in the case of my retired surgeon client, the IRR would be about -15.
The IRR answers the question "how did I do?" But it does not answer another important question: How did the portfolio manager do? The answer lies in the "Time-Weighted Return." As the portfolio manager has no control over when an investor might add funds to or withdraw funds from the portfolio, the time-weighted return is calculated based on the assumption that no funds are added to or taken from the portfolio during the time period being evaluated.
Consider the following example of two investors. They own the same fund -- let's call it Growth Mutual Fund-- over a five-year period. We want to calculate three things – what was Investor A's five-year return, what was Investor B's return, and what return should we credit the manager of the fund?
| Year 1: 10% | $100,000 (initial deposit) | $50,000 (initial deposit) |
| Year 2: -30% | Row 1 - Cell 1 | Row 1 - Cell 2 |
| Year 3: 20% | -$50,000 (withdrawal) | $50,000 (deposit) |
| Year 4: 15% | Row 3 - Cell 1 | Row 3 - Cell 2 |
| Year 5: 20% | $50,000 (deposit) | Row 4 - Cell 2 |
| Portfolio Value(end of 5 Yrs.) $104,712 | $104,712 | $145,556 |
So how did these two investors do, based on internal rate of return?
| Investors' Portfolio IRR Return | 0.80% | 7.90% |
Let's break these numbers down: The Internal Rate of Return calculations show that over the five-year period Investor B did far better than Investor A, as he was lucky in the timing of his investments into Growth Fund. Investor B only had $50,000 invested when the fund lost 30%, while Investor A had $100,000 invested.
Also, Investor A withdrew $50,000 at the beginning of year 3 just before the fund bounced back with a 20% return, while Investor B had just invested an additional $50,000.
However, as the fund manager had no control regarding the timing of these investments, the two IRR calculations provide no information regarding his or her performance. For that we need to look at the second measure, the Time-Weighted Return. As noted earlier, this is a calculation that assumes 100% of the investment was made on day 1 with no additions or withdrawals during the investment period.
Having reviewed the investment policy of Growth Fund, we have determined that the appropriate performance benchmark for the fund is the Standard & Poor's 500 Growth Index. Let's assume the return on the S&P 500 Growth fund was 4.2%.
| Row 0 - Cell 0 | Manager's Time-Weighted Return | 4.9% |
| Row 1 - Cell 0 | S&P Growth Benchmark Return | 4.2% |
Nice job, Mr. Fund Manager.
The Moral: monitoring performance is important, but equally important is to be sure you are using appropriate performance measurements.
Harold Evensky, CFP is Chairman of Evensky & Katz, a fee-only wealth management firm and Professor of Practice at Texas Tech University. He holds degrees from Cornell University. Evensky served on the national IAFP Board, Chair of the TIAA-CREF Institute Advisor Board, Chair of the CFP Board of Governors and the International CFP Council. Evensky is author of The New Wealth Management and co-editor of The Investment Think Tank and Retirement Income Redesigned.
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