Move over total return, it’s time to look at investor return

An abridged version of this article was first published in the HT Mint on February 22, 2013; Co-Author: Dhruva Raj Chatterji, Morningstar Indiahttp://www.livemint.com/Page/Id/2.0.1114338439

Mutual fund investors seem to be a disgruntled lot these days. It would not be fair to paint everyone with the same brush, but the overwhelming feeling we get via various forums is that mutual fund investors (especially on the equity side) are quite dissatisfied with the performance of their funds. Who’s to blame them really—after all the equity markets have pretty much not gone anywhere over the past 5 years, with the benchmark indices yielding flattish returns. For example, Sensex was around the 20,000 mark in the beginning of 2008, and it remains close to that mark, five years hence. Although there may be a time period bias here (of looking at a point-to-point period), there is no doubt that the patience of equity fund investors has truly been tested over the past 5 years, especially for those that have remained invested.

Retail Investors Have Typically Not Been Good Market-Timers

The time of entry also becomes a crucial factor in gauging the investor experience. After all, retail investors have historically not been good market-timers, whether in India or globally. As renowned fund manager Prashant Jain, of HDFC Asset Management points out in various forums, retail investors tend to usually enter the market in higher volumes in the last leg of the rally, when the markets have already moved up significantly and P/E multiples are higher.

Barber, Odean and Zheng (2003) in their research find that investors ‘over-optimistically’ bet on past returns as an indicator of future performance (representative heuristic) when they buy mutual funds. On the other hand when they sell they tend to dispose of superior performers and to hold losing investments (disposition effect). Similarly, Fiotakis and Philippas (2004) find that in Greece, mutual fund investors are active trend chasers and their investment decisions are wrong and short-lived.

A look at equity fund flows and mobilization trends in Chart 1 and Table 1 support these arguments in the case of Indian individual investors too. In FY 04-05, equity funds registered a net inflow of only Rs. 7,293 crores, while the Sensex hovered between levels of 5,500 – 6,500 during the year, and was available at attractive valuations. Flows picked up considerably in FY 05-06 and breached the Rs. 31,000 crores mark. The number of equity fund folios (which is an indicator of number of investors) also grew by more than 80% during the year. Over the next two financial years, the flows and mobilization of equity funds remained robust and continued to grow. During FY 07-08, the net inflows of equity funds were the highest at almost Rs. 41,000 crores, even as the Sensex climbed to a peak of around 21,000 in January 2008, before dropping to around 15,600 levels by the end of March 2008. The number of equity folios crossed a record 3-lakh mark, and grew by 46% during the financial year.

Despite the absolute quantum of inflows being the highest in FY 07-08, the organic growth rate (inflows as a percentage of beginning assets) was actually the highest at 86% in FY 05-06, when the Sensex was at much more attractive levels. This indicates that despite the relatively smaller size of the industry then, there were many investors who invested in FY 05-06, and would have benefited because they entered at the beginning of the rally. In FY 07-08 the organic growth rate was a healthy 36%, but considerably lower than that of FY 05-06. However, that doesn’t disguise the fact that investors continued to pour money into equity funds in FY 07-08 even as markets breached new highs, and elements of froth became more evident.

We can see from Table 1, that an investor who got in at the last leg of the rally would have lost about 48% in a single year, and hence this would have been quite disappointing, in spite of the funds claiming to have performed well in terms of total returns over a 5-year period. For the growth of the asset management industry, the investor experience is quite crucial, and that will also help to expand the acceptance of mutual funds, especially among retail investors. A good barometer for measuring investor experience is “Investor Return”. 

Table 1: Equity Fund Flows and Purchases and Performance Indicators
Financial Year	Net Flows  (in Crs.)	Mobilization (in Crs.)	Flows as % of beginning assets (Organic Growth Rate)	Total Equity Assets (in Crs.)	Year-end Equity Fund Folios	Return from Sensex	Growth of Rs 10,000
FY 04-05	6,454	37,684	27	36,757	7,976,453	14.95	11,495
FY 05-06	33,173	83,485	90	92,867	14,622,070	55.23	17,845
FY 06-07	22,552	88,482	24	113,386	20,887,341	13.71	20,292
FY 07-08	40,782	119,838	36	156,722	30,592,281	18.99	24,146
FY 08-09	1,056	29,481	1	95,817	32,946,794	(47.70)	12,627
Source: AMFI, SEBI (Excludes ELSS category)

What is Investor Return?Investors often tend to suffer from poor market timing and planning, as highlighted above. A fund’s total return reflects a buy-and-hold strategy. But in reality you have different investors subscribing or redeeming from the fund at different points of time. So the actual return earned by an investor may be quite different from the total return that the fund displays.

Investor Return, according to Morningstar’s definition, "measures how the average investor fared in a fund over a period of time. Investor return incorporates the impact of cash inflows and outflows from purchases and sales and the growth in fund assets". It takes into account the fact that not all investors would invest and redeem at the same time. Hence it places a higher weight to returns when assets invested are higher and lower weight to returns when assets invested into funds are lower. As with an internal rate of return (IRR) calculation, investor return is the constant monthly rate of return that makes the beginning assets equal to the ending assets with all monthly cash flows accounted for.

Lets explain this with the help of a hypothetical example:

Table 2: Hypothetical Example of Fund A
Month	Monthly Total  Return %	Growth of Rs. 10,000	Total Net Assets (Rs. In Crs.)	Estd. Net Flow (Rs. In Crs.)
		10,000	273
31-Jan	1.00%	10,100	287	12
28-Feb	9.14%	11,023	323	9
31-Mar	8.98%	12,012	370	18
30-Apr	-2.60%	11,700	371	11
31-May	-4.57%	11,165	364	10
30-Jun	16.19%	12,973	453	29
31-Jul	-0.52%	12,906	499	49
31-Aug	9.80%	14,171	613	65
30-Sep	-7.54%	13,102	608	41
31-Oct	-3.78%	12,606	620	36
30-Nov	-15.32%	10,676	549	23
31-Dec	-2.96%	10,360	550	18

Fund A’s assets grew rapidly to Rs. 613 crores in August. Until then an initial investment of Rs. 10,000 in the fund had grown to Rs. 14,171. However, post August the fund started generating negative returns. Also, around 57% of the fund’s overall inflows for the year came in between August and December. Investors who purchased the fund in August clearly did not have the same experience as investors who bought the fund in January. Investors who bought the fund in January and remained invested made a total return of 3.60%. In contrast to total return, the investor return (or what the average investor earned) over this time period is -10.98%.

Minding the Gap is Important

Investor return is not a substitute for total returns, but can be used in combination with total return. The gap between investor return and total return indicates how well investors timed their fund purchases and sales. When investor return is less than total return, it means that investors didn’t participate equally in the fund’s monthly returns—more investors participated in the downside returns and less in the upside returns. This sometimes happens when investors chase returns and assets flow into a fund at its peak of performance.

To see how investors have fared in the United States, Morningstar calculated asset-weighted investor returns for fund asset class groups over the past 10 years (ended December 2010) and then compared it with the category averages. A behavior gap seems to be evident in all fund asset classes as per Table 3 highlighted below.

Table 3: Asset Weighted Returns over 10 Years (ended Dec 2010)
Fund Group by Asset Class	Investor Return	Total Return	IR - TR Gap
U.S. Diversified Funds	2.32	3.3	-0.98
U.S. Sector Funds	3.89	6.08	-2.19
Balanced Funds	3.96	5.13	-1.17
Intl. Diversified Funds	4.92	5.98	-1.06
Intl. Regional Funds	6.37	8.77	-2.40
Taxable Bond Funds	4.46	6.27	-1.81
Municipal Bond Funds	2.04	4.02	-1.98
Alternative	9.94	13.07	-3.13
All Funds	3.38	4.71	-1.33
Source:Morningstar,  Reflection on Fund Management - Five Lessons in 25 Years (Presentation by Don Philips)

According to Morningstar, “In addition to revealing patterns of investor behavior, investor returns can also shed light on how well fund families are preserving the investor experience. It is the responsibility of fund companies to promote sound investment strategies. If the fund companies are encouraging short-term trading and trendy funds, they may not be looking at investor’s long term interests. These fund companies are likely to have funds with low investor returns relative to total returns.”

Therefore, minding the gap over the long term is quite crucial. After all, the investor experience is paramount, to repose faith in equity-investing again.

The Application of Numeraire Portfolio in Pensions

This interview was first published by the Global Association of Risk Professionals on February 14, 2013

http://www.garp.org/risk-news-and-resources/2013/february/the-application-of-numeraire-portfolio-in-pensions.aspx?altTemplate=PrintStory

The complexities of pension fund management and maximizing retiree returns are compounded by "enormous risks," observes Eckhard Platen, professor of quantitative finance at the University of Technology, Sydney. "There is a need of a little bit of academic direction to do something about it. There is a way to do it. Even developed countries need to wake up and say, 'now something has to be done."Noting that classical finance theory has not filled all the gaps, Platen brings to the discussion a "Benchmark Approach" that, in a recent interview, he put in the context of a numeraire portfolio and how it could be applied to the practical issues and concerns surrounding pension schemes. At UTS Sydney since 1997 --as a joint appointment of its School of Finance and Economics and School of Mathematical Sciences -- Platen has been contributing to efforts to improve the pension system in Australia.

With a Ph.D. in Mathematics from the Technical University in Dresden and a Dr.Sc. from the Academy of Sciences in Berlin, where he headed the Sector of Stochastics at the Weierstrass Institute, Platen has written more than 150 research papers in quantitative finance and applied mathematics, and his books include "A Benchmark Approach to Quantitative Finance" (Springer, 2006).

This interview conducted by Nupur Pavan Bang, senior researcher, Centre for Investment at the Indian School of Business in Hyderabad, covers the evolution of Dr. Platen's views on diversification principles and risk neutrality, the numeraire portfolio and practical approaches to pension investing.

You do not believe in the classical principle of no-arbitrage. That is the most fundamental principle of asset pricing theories in financial literature.

In the early 1990s, when I started working with leading investment banks in Australia, I was confronted, in practice, with the classical paradigm called the no-arbitrage pricing theory. Over time, it became clear to me that this theory is too narrow; the assumptions made are too constraining, and we must have an alternative that is more appropriate, especially in the case of longer-term contracts. It just occurred to me that something is wrong. The classical notion of no-arbitrage restricts too much the modeling world. There is a less restrictive and economically very reasonable notion of arbitrage that one should use. In principle, we should be able to create financial contracts and hedge them in a way that is less expensive than what classical theory propounds. Over the years, I was able to demonstrate how this is indeed possible.

Are pension schemes, therefore, very long-term contracts where you think your theory can be applied?

Think of it this way: Governments, companies and individuals contribute to pension funds. The amount is very big for most of us. As soon as we start earning, we are told that this contribution is mandatory. The cumulative contribution over the years is very significant, because if you start earning at the age of 20, you will end up contributing for 40 to 45 years. Lots can be done with this money from the time when the contribution is made and the payoffs are really paid off.

What are the concerns with the traditional pension schemes? What went wrong?

It is an enormous challenge to gauge a developed market and an emerging market in the same light. To start with, the way pensions have developed, they have emerged as the core of the welfare system. Secondly, the defined benefit pension plans have failed in the countries of the West. Thirdly, large companies like General Motors and Ford are just pension-generating companies, nothing else. Fourth, governments organize pensions based on an average mortality.

The aging population is a concern in a lot of countries. Let's say people live longer -- say, 15 years longer on an average. The calculations completely go wrong. Also, some major industries of some countries or some economies, they may just decay or vanish. We have seen this many times. For example, if a pension scheme invests a big chunk of the money in, say, a mining group in Australia. It could happen that after 15 or 20 years, the mining action shifts to Africa. What do you do then? So it would be very good if a scheme is widely diversified, so that its performance does not depend on a single industry or nation.

There are many different types of contribution schemes nowadays. Doesn't that solve the problem?

No. Look at the equity-based contribution schemes that are now very popular in the developed nations. They often force people to liquidate everything at retirement date and buy an annuity. If the market is down in a particular year, and equities form 40% of the pension, then that is enormous risk. I would say this has to be removed soon.

What can be done?

One thing that should not be done is setting up a defined benefit scheme. Because you can never guarantee payoffs at the end of 5, 10 or 30 years. But what one can do is pool all the knowledge and best practices to create a mutual scheme or a pension scheme. The scheme should be diversified in terms of age of the participants, and it should have a large base of participants. Then keep adjusting the payoffs from time to time, depending on changes in life expectancy and economic conditions. So we aim to get the highest possible payout in the least expensive way. The challenge is how to set up such a scheme and make it fair so that, in principle, it is fully transparent to everyone.

How can such a scheme be set up?

There are different contribution plans that give different choices at retirement. This has to be put on the table. That is, if one contributes a certain amount in cash, then something will be done with that cash. It will be invested using certain strategies that target the highest possible payout. When you retire, you will get a payoff stream, like that of a life annuity, in cash. There is an agreement in principle that you get payments only until you die.;;

This pension has to be fully sustainable, fair and, of course, globally diversified. Since the level of payouts cannot be fully guaranteed, it should be a targeted life annuity. The entitlement depends on how much one paid in -- how many units of the life annuity one has purchased over time by contributions to the scheme. The assets and liabilities are matched regularly over time, using what I call real-world pricing. They are adjusted periodically, based on the latest mortality figures and model adjustments available.

In some countries -- for example, India -- the regulations do not allow for global diversification of the pension pool.

Yes, certain countries have certain regulations, and one can operate only under these regulations. I believe the policy in India is to very much keep pension funds inside the country. It may be too early now, but there will come a time when the authorities will realize the advantages of diversifying beyond the country.

Can you explain your approach in more detail?

I use the Benchmark Approach, a kind of more general framework that we have today in finance. It does not take anything away from existing classical theory. John Larry Kelly Jr., of Kelly criterion fame, published a paper, in 1956, founded on maximizing expected portfolio growth based on logarithmic utility and gambling contracts.

In July 1990, theJournal of Financial Economics,a mainstream finance journal, published "Numeraire Portfolio," a paper by John Long Jr. This is a portfolio which, when taken as a "numeraire" or a benchmark, and some given portfolio is denominated in units of this benchmark, then the current benchmarked value of the portfolio is greater than or equal to its expected future benchmarked values. Using this insight, we can potentially get a fair benchmarked portfolio process, forming a so-called martingale, where the current benchmarked value is equal to the expected future benchmarked values. I am suggesting to search always for this least expensive portfolio to hedge future payoffs. When doing this, use the real-world pricing formula, assuming that there exists a numeraire portfolio -- the benchmark -- and the expectations are taken under the real-world probability measure that models future change.

Doesn't most of the financial literature use a risk-neutral probability measure?

Yes. Almost 90% of the literature. But I don't believe that the risk-neutral probability measure exists. In fact, I know that this measure does not exist when fitting long-term models. Parts of the industry see the problem too, and that is why the largest reinsurance company in the world is interested in what I found.

I can tell you that I am a non-equity premium puzzle person, because the modeling world that the Benchmark Approach provides is so rich that a high equity premium is not a puzzle at all. It's like you want to force a classical risk-neutral model [to calculate a risk premium] onto something where, in principle, you should accept and use the observed risk premium, which is higher than the classical theory allows. It is just another indication that the classical theory is too narrow.

How does your theory compare with the classical theory?

While we don't take anything away from the classical theory, we go into a richer modeling world by making a very simple assumption: that there exists a numeraire portfolio. The numeraire portfolio, when used as a benchmark, makes all benchmarked non-negative portfolios supermartingales -- their current benchmarked value is greater than or equal to the expected future benchmarked values. The greater-than-or-equal sign indicates the crucial supermartingale property. Since this property holds for all non-negative benchmarked portfolios, one can say that the numeraire portfolio is the best portfolio in this sense. It performs so well that when used as a benchmark, it forces all non-negative portfolios in expectation down, besides those that are martingales. With the supermartingale property, and no extra assumptions, I can prove that this portfolio in the long run outperforms any portfolio. It's a dream portfolio.

It is also the portfolio that maximizes the expected logarithmic utility. It is growth-optimal. It's a portfolio that in the shortest time reaches a certain level. It is the portfolio that cannot be systematically outperformed in any time period by any other portfolio. All these properties are model-independent and, thus, very robust. In fact, even the Indian market, if you take a close look at it as an investment universe, has its own numeraire portfolio somewhere, extremely well-performing. The question is just to find and construct it.

How do you account for the down side?

If I look with the Benchmark Approach beyond the classical theory, then there are some classical arbitrage opportunities in this richer modeling world. However, these are strategies and portfolios where I have to allow, for certain periods, some probability to become negative. But I argue that it is not necessary to exclude those strategies. We should look only at non-negative portfolios, because, with a notion of reasonable economic sense, when the worth of market participants becomes negative, then we have to remove them from the market because they are bankrupt. We take limited liability into account, but there is no need to look at the negative portfolios and exclude arbitrage for these.

This supermartingale property is also in this respect very elegant and powerful. It provides the simple mathematical conclusion that any non-negative supermartingale that reaches zero will never get out of zero. In this sense, one cannot create out of zero capital some positive wealth with a non-negative portfolio. This type of arbitrage, called strong arbitrage, is then automatically excluded in the wider modeling world of the benchmark approach.

How do you construct the numeraire portfolio?

The numeraire portfolio is very diversified -- the best diversified portfolio you can build. In principle, it is capturing the non-diversifiable risk of the market that follows from a theorem that I have. Of course, this clings very much to the classical theory. Harry Markowitz once told me that I should call my theorem the Diversification Theorem, which brings all the finance theorems and principles together.;;

Using this diversification theorem, I create, in its simplest application, an equally weighted index (EWI), equi-weighted over companies, industries and countries. This index has a higher growth rate and higher Sharpe ratio (as well as lower volatility) when compared to the index weighted by market capitalization. It is a better proxy for the numeraire portfolio than the market-cap-weighted index. It can be used directly in portfolio management, as a best performing portfolio, as a benchmark.

The larger the number of companies, the closer we get, in principle, to the numeraire portfolio. The fundamental Law of Large Numbers is at work here. The market needs to be well securitized, which is a very simple and easy condition. In a well-securitized market, with an increasing number of securities, the sequence of equally weighted indices is a sequence of approximate numeraire portfolios. This is something that is covered by the Naïve Diversification Theorem.

How does the numeraire portfolio work as an investment strategy?

The strategy of an EWI is to buy low and sell high, and if a market is always trending up, you get people only wanting to buy and not to sell. But this fund will sell in such a scenario. On the other hand, if the market crashes, this fund will buy. So it has a very stabilizing effect on the market. The systemic risk in the market, with this kind of portfolio on a macroeconomic scale, is reduced.

Then there are people who might say, "All this is good, but what about transaction costs?" At 40 or 80 or even 200 basis points, the performance, of course, goes down but this portfolio still performs better than the market-capitalization-weighted portfolio. The Sharpe ratio is still better for the proxy of the numeraire portfolio. It is a very robust, stable kind of situation.

How can the pension fund industry use the numeraire portfolio?

The pension fund must invest in a proxy of the numeraire portfolio. Not just that, but the numeraire portfolio also gives us a pricing rule. In the supermartingale world, we call it the fair price process. Let's take a savings account; and also a proxy of the numeraire portfolio, a benchmark; and let's benchmark the savings account. Over the long term we get an on-average downward-sloping fluctuating curve for the benchmarked savings account, because the numeraire portfolio is going up more in the long run than the savings account. So this is a self-financing portfolio. Financial planning tells you that when you are young you should invest in the equity market (the benchmark), and then in later years fixed income (the savings account).

Using the numeraire portfolio and the savings account, about which I just spoke, we can construct a self-financing hedging strategy, where according to some model, you invest almost everything into the numeraire portfolio when you are young and then slide over, in a precisely defined manner, to the savings account over time.

Does this portfolio take care of inflation? In a country like India, where inflation is on the higher side, people are worried about the time value of their money.

People like their pension payouts to be inflation-indexed. That is because the pension contract is very long-term and much can happen over that period. In my experience, interest rates are generally a percentage or two higher than inflation in most economies. It is very difficult over long time periods to get the interest modeled correctly. So why not take it out completely? What we do is assume that one unit of payment is equal to one unit of the saving account. All the payments that you contribute and get later on in your post-retirement stream are in the form of savings account units. In particular, the targeted payouts are units of the savings account. So when you purchase your life annuity, you get rid of the risk or uncertainties from the modeling problems coming from the short rate. My payout unit is the unit of the saving account; my basic instruments are the benchmark and the savings account.

Current actuarial methodologies focus primarily on modeling the interest rate evolution to value pension funds and life annuities. Several developed countries have moved to a zero-interest-rate regime. This creates problems for the growth of wealth when using classical actuarial methods. Using the benchmark approach and the proposed targeted pension, one can avoid several of the currently burning problems. In the design of new pension schemes, one can benefit in several ways.

Trend is your best friend

This article was first published in the Hindu Businessline, Investment World, February 10, 2013; Co-Author: Archana Mishra, NMIMS Hyderabad.

 

If prices follow a random walk, past prices cannot be used to predict the future prices. And prices do follow a random walk- this was and still is believed by most academicians and many professionals in the field of finance. This belief gives rise to the belief about the ineffectiveness of Technical Analysis as a tool for aiding trading decisions.

But the question is, do the prices really follow a random walk? The Efficient Market Hypothesis (EMH) has propagated that Technical Analysis is useless if the markets are even "weak form efficient". Lo and Hasanhodzic in their book, 'The Heretics of Finance' (Bloomberg Press, 2009) point out that, research shows, patterns do repeat themselves and identifying these patterns can result in forming profitable trading strategies.

Let us clarify at the outset, that we find the notion of EMH itself is questionable. Having said that, research in developed nations point towards at least weak-form efficiency of the markets. Which might be the reason why many fund houses reduced the number of chartists on their teams in the last two decades. For example, in 2005, Citigroup's Smith Barney unit let go of its entire team of technicians. "The clients no longer wanted technical analysis", reported Wall Street Journal.

In India, technical analysis is still very popular and investors are still fascinated by what the complicated looking lines have to say. Even the "Big Bull" of Dalal Street, Mr. Rakesh Jhunjhunwala said in an interview with the Economic Times, "I use a lot of technical analysis for trading at times".

While more and more analysts and investors are preferring to use fundamental analysis, technical analysis has its own share of loyal chartists in India. Research on the Indian bourses give mixed results, with some of them indicating that price movements in India may not be even weak form efficient, making Technical analysis relevant in the Indian context.

Typically, long term investors like to use fundamental analysis, while traders use technical analysis along with fundamental analysis. However, loyal chartists believe that the charts reflect long term trends too as fundamentals are reflected in price movements.

It is advisable for any trader to look for the following indications before taking any position:

a)      Look for the Trend: first check whether the stock has an upward trend or downward trend. If the trend is upward then take a long position. If the trend is downward, then take a short position.

b)      Look for the indicators: After analyzing the trend, look for indicators accordingly. If the stock has an upward trend, then look for buying indicators such as hammer, morning star, morning star doji, bullish engulfing etc. If the stock has a downward trend, then look for sell signals such as hanging man, bearish engulfing, evening star, shooting star, shooting star doji etc.

c)       Look for Confirmation Candle: If the candlestick chart is used, then after the indicator look for confirmation candle to occur. For the buy indicator, the confirmation candle should close higher than the high of the indicator. While for the sell indicators, the confirmation candle should close lower than the low of the indicator candle.

d)      Look for Volume: The confirmation should always be followed by large volume either at the indicator candle or the confirmation candle.

e)      Verify by using various trading tools: MA, MACD, DMI, Fastk, RSI, Pivot are few of them.

After getting positive indication of the trend from the aforementioned steps, take the position (buy or sell) with stop loss below the low of confirmation candle for buy positions and above the high of confirmation for sell positions.

There are various patterns which may be formed by the prices. A few popular one's are the head and shoulder, triangle, rectangle, flag. Patterns are difficult to find. But once you find them, it's worth the effort.

There is no tailor made ideal way to invest. It really depends on the individual’s comfort level in using the technical analysis tools, or analyzing the fundamentals to take positions. However, one should ensure that at least 3-4 indicators are in sync with each other before taking a decision.