The dot represents the average expected return. This shows the much greater potential for downside in higher risk portfolios. In the short-term, the dominant driver of loss size is the variance of the portfolio. What if we take those same portfolios, and invested for longer periods of time?
As we invest for longer and longer, the mass of probability smears upwards: our upside odds improve. The dots on each graph correspond to the 20th, 50th, and 80ths percentile outcomes in each case.
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Note how initially the bad outcomes involve losses, but over time even the worse cases gets better? Sometimes even positive? But the median and good outcomes are substantially higher. Similar downside, better upside. In the long term, the average matters more. This is why time horizon is such an important part of determining the right risk level for an investor.
I used very simple, straightforward assumptions about the risk and return here. This is a wonderful way to depict risk and its effect on likely return distributions. I have always wondered how many investors really understand the dispersion in their strategies. Really nice work. Free E-filing.
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Realistic risk and return
Start Your Tax Return. The value of the portfolio at the end of each sub-period is adjusted for the external flow which takes place immediately before. External flows into the portfolio are considered positive and flows out of the portfolio are negative. Note also that if the portfolio is valued immediately before each flow instead of immediately after, then each flow should be used to adjust the starting value within each sub-period, instead of the ending value, resulting in a different formula:.
The term time-weighted is best illustrated with continuous logarithmic rates of return. The overall rate of return is the time-weighted average of the continuous rate of return in each sub-period. The continuous time-weighted rate of return over the ten-year period is the time-weighted average:. The ordinary time-weighted return over the five-year period is:.
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The result is then annualized over the overall five-year period. Investment managers are judged on investment activity which is under their control. If they have no control over the timing of flows, then compensating for the timing of flows, applying the true time-weighted return method to a portfolio, is a superior measure of the performance of the investment manager, at the overall portfolio level.
Internal flows are transactions such as purchases and sales of holdings within a portfolio, in which the cash used for purchases, and the cash proceeds of sales, is also contained in the same portfolio, so there is no external flow. A cash dividend on a stock in a portfolio, which is retained in the same portfolio as the stock, is a flow from the stock to the cash account within the portfolio. It is internal to the portfolio, but external to both the stock and the cash account when they are considered individually, in isolation from one another. The time-weighted method only captures the effect attributable to the size and timing of internal flows in aggregate, i.
This is for the same reason, which is the time-weighted method neutralizes the effect of flows.
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It therefore does not capture the performance of parts of a portfolio, such as the performance due to individual security-level decisions, so effectively as it captures the overall portfolio performance. The time-weighted return of a particular security, from initial purchase to eventual final sale, is the same, regardless of the presence or absence of interim purchases and sales, their timing, size and the prevailing market conditions.
It always matches the share price performance including dividends, etc. Unless this feature of the time-weighted return is the desired objective, it arguably makes the time weighted method less informative than alternative methodologies for investment performance attribution at the level of individual instruments.
For performance attribution at individual security level to be meaningful in many cases depends on the return being different from the share price return. If the individual security return matches the share price return, the transaction timing effect is zero. Let us imagine an investor purchases 10 shares at 10 dollars per share. Then the investor adds another 5 shares in the same company bought at the market price of 12 dollars per share ignoring transaction costs. The entire holding of 15 shares is then sold at 11 dollars per share. The second purchase appears to be badly timed, compared with the first.
Is this poor timing apparent, from the time-weighted holding-period return of the shares, in isolation from the cash in the portfolio? To calculate the time-weighted return of these particular shareholdings, in isolation from the cash used to purchase the shares, treat the purchase of shares as an external inflow. Then the first sub-period growth factor, preceding the second purchase, when there are just the first 10 shares, is:.
Time-Weighted Rate of Return – TWR
The poor timing of the second purchase has made no difference to the performance of the investment in shares, calculated using the time-weighted method, compared for instance with a pure buy-and-hold strategy i. Other methods exist to compensate for external flows when calculating investment returns.
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Such methods are known as "money-weighted" or "dollar-weighted" methods. The time-weighted return is higher than the result of other methods of calculating the investment return when external flows are badly timed - refer to Example 4 above.
One of these methods is the internal rate of return.