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Rolling Returns of Mutual Funds can be a useful tool for SWP

Oct 31, 2016 by Dwaipayan Bose | 63 Downloaded
Picture courtesy - PICJUMBO

Systematic Withdrawal Plans (SWP) is increasingly gaining currency with Indian mutual fund investors, at least, based on the response received from our readers to many SWP related content posted on our website (www.advisorkhoj.com) over the past few months. SWP is a fantastic mechanism for investors who want regular cash-flows from their mutual fund investments. SWP provides you with a mechanism of generating fixed cash-flows from your investment, at regular frequency (at a fixed date even) to meet your regular expenses. All withdrawals made one year from the date of investment in equity mutual funds are exempt from capital gains taxation. After you make your regular withdrawals, the balance investment continues to earn returns and compound to create wealth for you.

Challenge of determining SWP withdrawal amount

One complex challenge that investor must understand with respect to SWP is to determine the withdrawal amount. There are two important, and sometimes conflicting, imperatives. The first consideration is that your SWP amount should be able to meet your cash-flow requirements. Your cash-flow needs are specific to your personal situation, and therefore there can be no general formula to determine how much money you need from your investment every month; you need to determine, how much money you need. The second important consideration is that, your regular withdrawals from your investment should not deplete the initial investment too quickly.

You should understand that, the fund house gives you SWP cash-flows by redeeming units of your mutual fund investment and therefore, in an SWP you are left with diminishing unit balances. If your withdrawals are more than the average rate of returns, then you will be left with a depleted investment base.

Another issue that investors have to grapple with SWP from equity or equity oriented funds is volatility; SWP in very volatile markets can cause big depletions of your unit balances and consequently would take that much longer for your investment values to recover. In this post, we will discuss an analytical framework for your SWP withdrawals, so that your capital amount, to a large degree is not diminished, for prolonged periods of time.

Rolling Returns

The foundation of the analytical framework that we will discuss in this post is rolling returns. If you are a regular Advisorkhoj blog reader, you will know that, rolling returns is the best measure of mutual fund performance. While other mutual fund performance measures, like trailing returns or point to point returns may have timing related biases, rolling returns have no such biases. Rolling returns, over a sufficiently long time period, provides us with a view of the range of return scenarios. The chart below shows the monthly rolling returns of a balanced mutual fund over the last 20 years. We are trying to illustrate a concept here and so the name of the fund is not important.


Monthly rolling returns of a balanced mutual fund over the last 20 years

Source: Advisorkhoj Research


We have shown monthly rolling returns because we have assumed that the SWP will also be monthly (if SWP is quarterly then you should use quarterly rolling returns). The monthly rolling returns show you all possible scenarios of monthly returns from the fund in the 20 years. Your objective is to determine a monthly withdrawal amount that ensures to a great extent that your investment does not fall below the amount invested by you value; in other words, you are trying to preserve capital as much possible. Please note that, it is not possible to ensure 100% capital preservation because equity markets are volatile and it is not possible to accurately predict volatility. With that caveat, to preserve our initial investment, we should try, as much as possible, to make our monthly withdrawals only from the capital gains and not from the capital amount. This is where rolling returns are useful.

If we are able to determine a range where monthly rolling returns are most likely to be, we can determine how much monthly withdrawal we can make, without depleting our capital. Please note we said that, we want to determine a range of most likely rolling returns and not average rolling return. If you base the SWP on average rolling returns, your capital will be preserved on an average over the SWP period; on the other hand, if you use most likely rolling returns, your capital is likely to preserved most of the times. By definition, average signifies 50% likelihood of occurrence; for an investor trying to preserve his / her capital as much as possible, 50% likelihood of occurrence is not most of the times. Therefore, we are reiterating the importance of determine a range where monthly rolling returns are most likely to be. This is what we will try to determine using two methods.

Visual examination of rolling returns chart

Please observe the rolling returns chart above. The maximum monthly rolling return is nearly 30% and the minimum monthly rolling return is nearly -20%. But, if you observe the rolling return chart more carefully, you will notice that, monthly rolling returns were between 0 to 5% most of the times. 0 to 5% is still a wide range, but it is much narrower than -20% to 30%. There were times when monthly rolling returns were more than 5%, but there were times when it deviated below zero. Deviations above 5% is good for you, because your money is growing, it is deviations below zero, which is of concern, if you want to preserve your capital. So what is the most likely monthly rolling return, with a bias towards conservativeness?

It is very difficult to determine simply by visual examination; however there are statistical tools that can help us determine, probabilistic scenarios of rolling returns, which in turn will help you plan your monthly withdrawals such that, you investment value is less likely to fall below your investment amount.

Statistical analysis

Like most random variables in the world, we can assume rolling returns over a long period of time to be distributed in the form of a bell curve (normal distribution), from which we can derive statistical inferences with respect to probabilistic boundaries of investment returns. We had explained the statistical significance of the bell curve or normal distribution in some or earlier blog posts, but we will briefly explain it again for the benefit of our readers who are familiar with bell curve (normal distribution).

The theoretical foundation of bell curve or normal distribution of returns is that, expected returns are clustered around the average return and the likelihood (probability) of deviations from the average tapers as the deviations become larger and larger, both on the positive (higher returns) and negative sides (lower returns). The chart below (more specifically, the area under the curve) shows the probability distribution of various ranges of returns.


More specifically, the area under the curve


In the chart above, µ is nothing but the average and σ is the standard deviation (SD). From the above chart, we can interpret that there probability of expected returns being higher than µ - 1σ is 84.13% (area under the curve to the right of µ - 1σ = 34.13%+34.13%+13.59%+2.28%). Therefore, if our monthly withdrawal is µ - 1σ % of the investment, we can be 84% confident that, the investment value will not dip below the initial investment amount. In our opinion 84% is fairly high confidence level; if you want higher confidence level for capital protection, you should ask yourself, if equity is the right asset class for you.

The 20 year average monthly rolling return of the balanced fund that we are discussing in this post is 1.8% and the 20 year monthly standard deviation is 5.5%. We need to annualize both the average returns and the standard deviation of returns. The annualized average monthly return (assuming monthly compounding) is 23.7% and the annualized monthly standard deviation is 18.9%. µ - 1σ implies that, your annual withdrawal should be 4.8% per year, or 0.4% (40 bps) every month. At this SWP rate, as per stochastic (probabilistic) framework, we should be able to preserve our capital most of the times.

Back-testing our stochastic framework

Stochastic frameworks / models are good intellectually, but do they stand the test of reality? We will know, only if we back-test the model in the market. Let us assume that, we invested 10 lakhs lump sum in the above-mentioned balanced fund, 10 years back (on 31/10/2006). As per our stochastic model our monthly SWP amount should be 0.4% of the investment ( 4,000 / month). Let us now see the cash flows of the SWP from 2006 – 2016.


Cash flows of the SWP from 2006 – 2016

Source: Advisorkhoj Research


The current value of the investment after 4,000 SWP / month is 29 lakhs; the investment has now trebled in value. Please focus your attention on 10 lakh line (the original investment) on the chart. The investment value has dipped below 10 lakh very briefly in the last 10 years. The investment value dipped below the original investment in only 9 months in the last 10 years.

Conclusion

If you think that our monthly SWP amount was too small ( 4,000 / month from an initial investment of 10 lakh) it is because we were fairly conservative in our approach (likelihood of returns being higher than average minus one standard deviation is around 84%). If want, you can be slightly less conservative and fix your SWP amount at average minus 0.75 X standard deviation. Your monthly SWP amounts will double (around 8,000 / month), but the likelihood of investment value dipping below the investment amount during the SWP period will also increase slightly. However, even if your SWP rate is µ - 0.75σ % of investment, the likelihood of monthly returns being higher than µ - 0.75σ % is nearly 78%. You can look up probabilities associated with various standard deviation percentages from a normal distribution point and determine what you are comfortable with, but remember as you go closer to the average the risk increases. In this post, we discussed how you can use rolling returns and standard deviations to determine your SWP amount.

Mutual Fund Investments are subject to market risk, read all scheme related documents carefully.

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Dwaipayan Bose

An alumnus of IIM Ahmedabad, Dwaipayan is a Finance and Consulting professional, with 13 years of management experience, mostly in MNCs like American Express and Ameriprise Financial, both in India and the US. In his last role, he was the Chief Financial Officer of American Express Global Business Services in India. His key interests are building best in class organizations, corporate governance and talent development

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