POST MODERN PORTFOLIO THEORY FOR A FICTITIOUS INVESTOR

HOW TO GROW YOUR MONEY FROM ONE MILLION TO FOUR in 15 YEARS!!!

quote: "Success is a thought process, positive thoughts create positive outcomes"

1 EXECUTIVE SUMMARY
This paper outlines the investment strategy for a client who has recently won S$1,000,000 via lotto. Our client Mr Lee, has asked us to evaluate his investment needs and recommend a portfolio of investments, which will ensure his financial freedom at retirement, plus ensure he has enough liquidity to ensure he can enjoy life.

This paper therefore analyses Mr Lee’s financial risk tolerance and recommends a portfolio of investments to ensure he meets his wealth goals. In making these recommendations we first outline the risks and rewards associated with the investing in various asset classes, and then make out recommendations by asset class.

In making our recommendations for Mr Lee’s portfolio of investments we use the Post Modern Portfolio Theory to structure the portfolio in such a way that returns generated by the portfolio consider the downside risks involved in investing in assets. This portfolio theory encourages investors to take less of a short term, risk averse approach to investing by highlighting the downside probabilities of failing to meet our long term investment goals. In constructing Mr Lee’s portfolio we have considered the information given to us about his investment horizon, liquidity constraints and financial risk tolerance.

We further our advice by outlining exactly how Mr Lee should go about building this portfolio of investments, including details of trading into individual asset classes.


2 INVESTORS OBJECTIVES AND PROFILE
Our investor is Mr Lee is a 40 year old sales manager on an expat assignment in Singapore. Mr Lee is married and planning children in the coming years. Both Mr Lee and his wife are of Hong Kong origin, however both were educated and spent their formative year in Vancouver Canada. Mr Lee has recently won S$1,000,000 in the lottery and is in search of investment advise that will ensure he and his wife are able to “slow down” by the age of 55. Even while he has won a lottery, he is also highly educated and is holding a very senior position within the company. Mr. and Mrs. Lee saves 30% of their combined annual salary of S$300,000 and have S$500,000 savings and do not see themselves needing to dip into their investment funds.

We interviewed Mr Lee to gauge his risk profile as an investor and to get a better understanding of his investment goals and objectives. Mr Lee’s investment goals are standard for someone who has recently won lotto, however he is not planning to take excessive amounts of time off in the near future.

As a reward for deferred gratification, Mr Lee wants to be certain that he has S$110,000, which he sees as money to be used for personal consumption in five years time. He is prepared to forgo greater gains to ensure he has the liquidity & flexibility to meet this personal commitment.

Using AMP’s risk profiler we have established that Mr. Lee is a balanced investor and an average risk taker, achieving a score of 29. By plotting Mr Lee’s age and risk score on the graph below we get an indication of where AMP’s, Lifesteps Investment Programme would invest for Mr Lee.



Having determined Mr Lee’s risk profile, we put together an investment portfolio option which we believe is most suitable for Mr Lee. Our investment policy is approached from the perspective of wealth creation through the focus on value. In the long run, the mix of asset classes in your portfolio will determine your wealth. Not how you traded into and out of individual assets.

In assessing Mr Lee’s investment needs we have taken into account his risk tolerance, time horizon, liquidity constraints, tax concerns and legal factors.

3 EQUITIES

After understanding Mr. Lee’s goal for retirement, we confirmed with him our understanding is correct.
In order to achieve the investor’s goal of retiring with at least SGD$4m within 15 years, with an initial investment of SGD$1m, a CAGR of 9.68% (or Net Minimum Accepted Return (MAR) ) is required, net of taxes and costs. The investor’s investment horizon is 5 years with a possible extension to 15 years. Hence both the time horizons need to be considered.



Expected Future Value at End of Year 5 = $1,587,401

Expected Future Value at End of Year 15 = $4,000,000


This section evaluates the various equity classes and equity class types.


3.1 OUR METHODOLOGY



We listen to an investor’s financial goals and needs. From Mr. Lee’s needs, we formulate a Minimum Targeted Returns and check it against various empirical data on feasibility. We are acutely aware of human’s behavioural biases and preferences, as such we pass it through a very strict process to take out subjective judgement at the early stages of Strategy formulation.

However, in this posting, I have deliberately omitted detailed discussions around Fixed income and REITs discussions as I do not have time to compile them.

After forming our strategy, we then allow subject opinions where by and large are our collective experience come into play for the next stages of evaluations. We also supplement our own judgement with that of third party independent research houses such as Morningstar to form a concrete executable plan.

We aim to achieve the investor’s goal with the least possible risk by using research on Inferred data on Coefficient of Downside Deviation.

3.1.1 EMPIRICAL DATA ON EQUITIES RETURN
Our approach is to first check for feasibility of this minimum accepted return based on
empirical data to find the most optimum way to achieve the target returns. According to a study by S. Mukherji , for medium and high target returns, the optimal portfolio for long-term investors is to be fully invested in small stocks.



From the above table, based on a portfolio constructed for a target return of 8%, the actual real return is 14.17% for a 15 years holding period and 10.49% for a 5 years holding period.
During the period of evaluation, the annual inflation rate averages 3.17 .

HOLDING PERIOD ON RETURN: SANITY CHECK
Therefore, the actual nominal returns based on a portfolio constructed for a target return of 8%, the actual nominal return is 17.34% for a 15 years holding period and 13.66% for a 5 years holding period.



The sanity check however did not take into account the market valuation at the beginning time of the analysis. Hence the effect of timing on returns especially for a holding period of 5 years could be not as certain, while there if generally more returns certainty for a 15 years holding period as it smooths out market timing issues. Therefore we would need to assess timing risks on returns.

MARKET TIMING ON RETURNS: FIVE YEARS HORIZON
The investor is looking at a 5 years horizon as an exit point with the possibility to exit at 15 years. Therefore market timing is important.
John Rogers said, “successful investors do more than just analyse a company”. For Philip Fisher, there are also hints for timing stock purchases of companies that meet the investment criteria during “Start-up period of a substantial new plant” which “has depressed earnings and discouraged investors.” Or when there is a “bad corporate news: a strike, a marketing error or some other temporary misfortune.” Another successful investor Warren Buffet, also times the market and buys good businesses during stock market crashes or during periods of depressed stock market prices .

Notes
1 S. Mukherji, 2003, Optimal Portfolios for Different Holding Periods and Target Returns, Financial Services Review 12, 61-71.
2 --- ditto ---
3 John Rogers, Mar 2004, Learning from the Masters, Professional Investor, page 26-27.
4 --- ditto ---



During the period between the year 2000 to 2005, apart from AMEX, Russell 2000 and NYSE, all other indices on the above chart returned a negative value over the 5 years period. This chart is deliberately shown with time period 2000 to 2005 to highlight the perils of bad market timing. It is inherently difficult to time the market, therefore it is imperative to identify stocks with a lot protection against any downside and that are positively skewed in it’s returns distribution.



Chart: Russell 1000, Russell 2000, Russell 3000, NYSE Composite Index, S&P 500, Dow Jones Industrial Average and Nasdaq between Dec 1992 to Dec 2007, Chart created using Yahoo.com)
By investing with a 15 years time horizon, all the benchmarks hovered between a 250% to 310%. This roughly equates to 7.6% Annual Returns without consideration of dividends. However for anyone who bought during the internet bubble between the year 1999 and 2001, the returns are still negative today. During certain periods of increased optimism, investors tend to be exuberant about the market prospects and have elevated risk appetite. The price of stocks reflected expected future earnings. When the company’s earnings disappoint, the risk appetite disappear and the stock price revert back to the mean causing huge lost of capital value to investors.


If dividends are considered for S&P 500 and reinvested, the total annual returns for S&P 500 would be enhanced by slightly less than 2% per annum on average.





SIZE EFFECT ON RETURNS
Empirical data obtained from Fama & French (1992) shows that for all stock types between July 1963 to December 1990, the monthly returns average 1.23%. This is equivalent to 15.8% on an annualised basis.




Table: Monthly returns of stocks sorted by BV/MV versus Market-Cap (Size) categories, July 1963 – December 1990, Louis K.C. Chan and Josef Lakonishok, 2004, Value and Growth Investing: Review and Update, Financial Analysts Journal, Page 76, Table sourced from Fama and French (1992)

Looking at Large or Small Stock regardless of Book/Market category: -
• Large stocks monthly return is 0.89%, or 11.22% on an annualised basis.
• Small stocks monthly return is 1.47%, or 19.14% on an annualised basis.

STOCK TYPE (GLAMOUR OR VALUE) EFFECT ON RETURNS
Now simply by checking against monthly returns sorted by Book/Market categories, Category 1 (glamour) stocks have a 0.64% return while category 10 (Value) stocks have a 1.63%.
Looking at Type regardless of Market Capitalisation (Size): -
• Glamour stocks monthly return is 0.64%, or 7.96% on an annualised basis.
• Value stocks monthly return is 1.5%, or 19.56% on an annualised basis.

COMBINATION OF SIZE & VALUE EFFECT ON EARNINGS
From empirical data sourced from Fama and French (1992) and presented by , the combination of size and value return are: -
• LARGE VALUE gives monthly return of 1.18%, or 15.12% on an annualised basis.
• SMALL VALUE gives monthly return of 1.63%, or a whopping 21.41% on an annualised basis.

EARNING/PRICE EFFECT ON RETURNS
We go on to investigate the effects of earnings/price effects on returns.



Chart: S&P 500 with Bollinger Band and P/E Ratio, 13 Dec 2007, CNNMoney.com

Since the year 2002 and 2003 where the P/E peaked at above 40 times, where there is an economic downturn led by SARS, Bird Flu and various pandemics, earnings were decimated. As earnings recover quickly after the year 2003, P/E continue to drop while at the same time, the prices continue to rise. The P/E today of less than 20 times, looking at the past 10 years average is in face quite low. There is no indication of a bubble.

However, it must be cautioned that the US economy was at it’s 3rd longest economic expansion in United States history which has brought many earnings upside to stocks, which could account for the low P/E (excluding periods of major mobilizations such as during world wars I and II) which “started back in November 2001 just after the 9/11 terrorist attacks and the 2001 recession, which was brought on by the sharp stock market drop and tight financial conditions in 2000 . With a possible US economy slow down, both the earnings and P/E may also fall due to reduced risk appetite, thereby severely affecting the capital value.

Of course it would be natural to want to put all the investments into an investment segment that gives the highest potential returns. However it must be cautioned that the sub-prime has still to run it’s full course, the prospect of a global economic slowdown is almost certain. In a slowdown or a recession, large capitalised companies with larger cash flows and reserves are better able to withstand the impact of an economic slowdown or recession in the worst case scenario.

Foot Notes (Part 2)
Louis K.C. Chan and Josef Lakonishok, 2004, Value and Growth Investing: Review and Update, Financial Analysts Journal, Page 76.
U.S. economic forecast for 2007: cooling off but no recession, The Manufacturer US
Published: 07 Dec 2006, http://www.themanufacturer.com/us/detail.html?contents_id=4895

1.1.1 EQUITIES RISK
As equities shall form the largest portion of the total portfolio, it is important to match the investor profile with special emphasis to analysing the possibility of not meeting targeted returns and take the necessary protection against capital loss. We recommend going for non-cyclical segments and a global spread to diversify away country specific risks.

MACRO ECONOMIC RISKS
The average Market valuation (P/E) of stocks rise and fall as business confidence rise and falls. During the year prior to a recession in 1999, the P/E was trading at about 35 for S&P 500. Therefore it is important to assess where the bottom line is with regards to average P/E valuations of stocks in the recession years so as to get a gauge of the possible downside risk should P/E fall to as low as in previous recessions, the capital is always protected.

The US economy is expected to slow down in 2008 and 2009, consumer confidence is at an all year low of 87.3 (1985=100) while the present Situation index decreased to 115.4 and the expectations index declined to 68.7 . (Consumers account for some roughly 70% of the US GDP of US$1.4 Trillion) . Credit risks remains on the horizon with bank writing down assets on Special Investment Vehicles or sub-prime lending. However with the federal reserve’s monetary easing policy in Credit risk reduction bias over inflation targeting, we remain cautiously confident that the market will not be too adversely affected. US will likely in our opinion be able escape recession in 2008, though the growth may slow sharply. In the Asia pacific region, China’s GDP is expected to ease to 10% in 2008 and 9.3% in 2009 providing some support to Asian economies, though not able to completely offset the US economic slowdown.



There is some expected slowdown overall in the world’s economies, but for countries which have large reserves such as China, Hong Kong, Singapore, UAE, major oil producing countries and Australia which has low debt, there is large fiscal policy flexibility.

COUNTRY & CURRENCY RISK
Therefore in selecting a portfolio, we shun funds with a narrow segment focus on country or industry. As the funds would then search for good stocks only within the country specified, leading to opportunity cost on potentially lesser returns. As Singapore’s economy is small and fairly narrow in nature, we advocate country diversification through purchase of US based equity funds. Funds typically have Large Capitalisation companies in their portfolio, these companies tend to have global coverage hence the risk is spread out globally. Currency risk is likely to be muted as the investments are spread out globally and any fluctuations will cancel out somewhat (though not fully). For example, a loss in US dollar versus Singapore dollar is likely to be offset by better performance for US companies exporting goods and services and hence better earnings and market valuation. So we are neutral on currency for the longer term.

Foot Notes: -
The Conference Board, November 2007 Consumer Confidence Index, http://www.conference-board.org/economics/ConsumerConfidence.cfm.
The Economist, http://www.economist.com/countries/China/profile.cfm?folder=Profile-Forecast

SEGMENT RISK AND HOT STOCKS RISKS
In the example of NASDAQ in the year 2000, these segments fluctuate wildly, if you buy at a wrong time, massive capital values are lost. Investors are generally lured by “Hot funds” using the law of “small numbers” and projecting current returns into the future, driving up the capital value massive. We do not want to take the risk to buy over-valued funds/segments even though empirical data shows that they could have years of out performance relative to value segments before eventually reverting to the mean in the longer term.

BEHAVIOURAL BIAS RISK
Investors are not more rational now that they were in 1945 . Human still has the same fear and greed and could mistake good company for good investments, filters bad memories in favour of good ones, etc, . We do not want to be biased in our choices of investments. Our charter is to “NEVER LOSE MONEY” for the investor. And along with that, we created a methodology of screening funds with objective parameters. Naturally some aspects of selection will be subjective or experienced based, but being aware of the behavioural biases we largely minimise that risk also by looking at Downside variation.

RISK OF SUB-OPTIMAL FUND MANAGER & EXCESSIVE TRADING
According to (Dowen & Mann) an efficient manager should be able to operate a fund at lower cost. Funds should only trade when it is advantageous to the shareholder. In order to catch up on returns, some fund manager trade aggressively in an effort to catch up on lost ground. It could only lead to even higher cost if the trade did not succeed thereby inflicting more damage on returns or affecting the ability of the investor to meet his targeted returns.

ETHICS & COMPLIANCE
This is an area that is the one of the most critical. Fund managers should be acting in the best interests of their investors. Therefore a fund manager or fund rating agency and it’s close associates must declare their holdings and ensure that no conflict of interests arise in the companies in which they are writing about.

REGULATORY RISKS
There appear to be no particular high probability regulatory risks that we can see on the horizon. Singapore could tax earnings remitted from outside of Singapore.

SIZE & EXPENSE RATIOS
Dowen & Mann found that over time, the managers of larger fund families produce greater returns at lower cost . Returns increases and the expense ratio decreases, this indicate economies of scale, although (Latzko 1999) found that the benefits of economies of scale are exhausted beyond 3.5 billion. However, most funds do not pass on the savings to investors, in fact the expense ratio had soared from 0.76% in 1945 to 1.56% in 2004, “despite the substantial economies of scale in these economies, they have actually incurred higher costs of ownership.” According to morningstar average expense ratio reported for all funds is 0.98% of assets. The highest average expense ratio is 1.86% reported for aggressive growth funds, and the lowest was 0.58% for the California Municipal Bond funds.

However, as the funds selected are “Small Value”, it is important to choose a fund size that is neither too big nor too small, this is because there is a limited universe of small capitalisation companies, increasing the fund size may lead to more companies qualifying as good investments and thereby reducing returns. Therefore a fund’s charter is very important, if there are no investments meeting their strictest criteria, the fund must instead hold cash and not just invest in sub-grade investments to make up the numbers.

Although big fund size tends to have lower expense ratio, the valuation tends to be richer. Funds that have a “Big Value” investment style type must then buy big capitalisation stocks. Big stocks tend to be better covered by analyst, more favoured by the market and hence more expensive, thereby reducing potential future returns. The reason for such reduced returns is due to an “ecology” of agency factors at play in our opinion. Good growth companies or Big companies tend to get more press coverage and sometimes positive reviews. All these considerations play into the career concerns of Professional money managers and pension plan executives (see Lakonishok, Shleifer, and Vishny, 1992). The fund managers may find that touting such companies stocks or story-lines to individuals are an easier sell. All these agents at work drive up the prices of such big companies.

SAFETY MARGIN
In order to have a Margin of Safety we need to buy funds which are trading below it’s intrinsic value. In this case, trading below it’s book value with good growth prospects plus dividend growths prospects with strong financial strengths and business viability. But to find stocks that are trading at a MV/BV < 1 is very difficult and maybe in not enough quantity. The investment opportunity window is very small. Therefore it is even harder to find a fund with a composite average of MV/BV < 1. All good companies with positive growth should be trading at a premium to Book value. But we will take into account P/E, Growth rate, and a maximum MV/BV of less than 2. Where possible we will supplement our safety margin with non-tangible information and analysis.

"Foot Notes": -
5 Meir Statman, 2005, Normal Investors, Then and Now, Financial Analyst Journal.
6 H. Kent Baker, John R. Nofsinger, 2002, Psychological Biases of Investors, Financial Services Review 11 , pages 97-116.
7 Richard J. Dowen, Thomas Mann, 2003, Mutual fund performance, management behaviour, and investor costs.
8 R.J. Dowen, T. Mann / Financial Services Review 13 (2004) 79-91, page 280
9 John C. Bogle, 2005, The Mutual Fund Industry 60 Years Later: For Better or Worse?, Financial Analysts Journal, January/February 2005, page 16
10 (Morningstar pg 274, from the Morningstar Principia Mutual fund database with data last updated on March 31, 2003),
11 Benjamin Graham, Investopedia.com, http://www.investopedia.com/terms/m/marginofsafety.asp


DOWNSIDE RISK (DR) PROTECTION
We protect against downside using a top down view and a robust methodology as described in earlier sections.


Protection layer: Macro
We evaluate the macro economic conditions going into the next year and beyond to determine whether the prices and valuations are reasonable compared to historical trend.

Protection layer: Country and Segment Risks
We then look at individual countries and industry segment and check against whether they are undervalue or over value and whether specific investment opportunities exists.

Protection layer: Empirical data sanity check
We use empirical data to find the best risk-return categories. And we assess whether these historical empirical data can be used successfully under current investment climate.

Protection layer: Fund selection Criteria
We use a combination of the Benjamin Graham’s method of finding valuable stocks/funds and Philip Fisher’s idea of assessing a suitable market timing.

Protection layer: Morningstar rating system.
We supplement our approach with a third party independent rating system. We especially like the morningstar stewardship assessment. This rating provides us across the board assessment of capability of management. With a small sum of $1m to invest, we would not likely be able to get access to senior leadership of big companies. The morningstar rating system can be found on Morningstar .

LIQUIDITY RISK
Funds are usually not as actively traded compared to stocks. Funds typically cannot be traded quickly enough to prevent a loss in case of a falling market. This illiquidity usually results in a wider bid-ask spread, resulting easily in cost of 2% or more.

POTENTIAL CAPITAL GAINS EXPOSURE RISK
Singapore domiciled residents do not pay capital gains tax, however dividends are taxable.

LITIGATION RISK
Well managed fund with a high morningstar rating should be fair protection against litigation. Most litigation and fines are levered against inappropriate behaviour of funds or fund managers. But there is no way to gauge our exposure, perhaps all we can do it to stay vigilant to watch over expense ratio as well as fund management’s compliance and renewed ratings from independent sources such as Lipper and Morningstar.

MORNINGSTAR STAR RATING FOR RISK MANAGEMENT
To supplement the risk management process, we use morningstar Star rating system to screen the funds. There are also factors such as stewardship index which we really like as this provides an added dimension on top of evaluating hard financial data.

Footnote: -
12 Morningstar, Mutual fund data definition, http://quicktake.morningstar.com/DataDefs/FundRatingsAndRisk.html

However this exposes us to Type II error in the case where morningstar erroneously rate a fund 1 star or 0 star leading to us rejecting the fund where in fact the fund turn out to be a top performer. This error leads to a missed opportunity and is a cheaper risk compared to Type I error in which we take a fund for a 5 star fund, we purchase it, but in fact it turned out to be a failure. For Type I error, our stringent methodology should be able to minimize it.

1.1.2 PORTFOLIO SELECTION
I choose the morningstar fund screener as it is quite easy to use (no particular preference) as a basis for narrowing down the selection of funds. From empirical data analysis: -




DOWNSIDE DEVIATION COEFFICIENT (CDD) FOR EQUITIES




SMALL CAP VALUE FUND
Selection Criteria (SMALL VALUE)
• Fund group: All
• Morningstar Category: Small Value
• Ratings and Risk: 4 stars to 5 stars
• Portfolio turnover less than or equal to: 75% (Richard J Dowen, page 269)
• Expense Ratio: less than 1.2%
• Average market cap (US$mil): Greater than or equal to $250million.



As there is no demonstrable benefit of excess performance with high expense ratio13 . I have weighted heavily a focus on Low expense ratio in the selection criteria. High earnings growth rate will likely lead to better chances of capital gains while low P/E with a high morningstar rating protects capital loss in case of any downturn in the economy. (Louis K.C. Chan and Josef Lakonishok, page 204) says that value stocks out-perform glamour stocks across all eligible stocks. And it was found that small cap segment of value stocks returns are even higher than big cap value stocks. It was conjured that mis-pricing patterns was more pronounced in the small-cap segment, which could be due to lack of analyst coverage. Thereby a focus of small cap value could yield richer opportunities than big cap value. However the exact reason for the mis-pricing is still being debated in the academic circle.
These are very rough selection criteria that returned 69 qualified funds.
Ken French says that you can’t beat the market. And excess performance cannot be easily measured between one fund and the other as different fund with a different focus chooses a different benchmark. Most fund managers will mirror their selected benchmarked with some minor differences. As a result most fund do not significantly outperform or lag the index in which they are being benchmarked. And there is no commonality in comparing different funds which track a different benchmark since they cannot be compared apples for apples.

Foot notes: -
12 R.J. Dowen, T. Mann, 2004, Mutual fund performance, Management behavior, and investor costs, Financial Services Review 13, 2004, pages 79-91, Hypothesis 2.

Therefore we recommend selecting funds based on Ethics and Star Ratings with higher weighted focus on Low P/E, emphasis on 5 Year returns and low expense ratio. The funds we have in mind are value funds with Average P/E tracking below the average S&P 500 historical P/E.



LARGE CAP VALUE FUND
Selection Criteria (BIG VALUE)
• Fund group: All
• Morningstar Category: Big Value
• Ratings and Risk: 4 stars to 5 stars
• Portfolio turnover less than or equal to: 75% (Richard J Dowen, page 269, too much trading activity is negatively related to returns)
• Expense Ratio: less than 1.2%
• Average market cap (US$mil): Greater than or equal to $250million.







1.1.3 TAXATION
The Securities Exchange Commission (SEC) has mandated that funds must reveal the Potential Capital Gains Exposure (PCGE) to investors and allow the investor to choose the most tax efficient way in which to pay for the Capital gains. Singapore tax residents do not pay capital gains tax.


2 PORTFOLIO ALLOCATION
We considered the fictitious Mr. and Mrs. Lee as investors with moderate risk profiles. However has they have aggressive savings rate, they have revealed that they are able to stomach some short term risks and volatility. Therefore we propose to use Post modern portfolio theory (PMPT) to optimise their portfolio. In doing so, we calculated inferred Cooefficient of downside deviation to obtain a portfolio that may have higher volatility, but towards a 5 years or 15 years horizon, have large margins of downside protection.

We have hypothetically structured a portfolio consisting of 10% Bonds, 10% REITS, 40% Small Capitalisation Value Equities and 40% Large Capitalisation Value Equities. Large Cap value balances against the more volatile Small cap value as empirical data shows that Large Cap value holds out better during a downmarket.

2.1 MINIMAL ACCEPTABLE RETURN AND DOWNSIDE RISK
Mr Lee’s stated investment goal is to have S$4,000,000 in 15 years time. This equates to a MAR of 9.68% over the investment horizon, as seen in the below graph. The graph also plots the expect return for each asset class. In our academic studies, we



Downside risk is a composite of three sub measures, namely, downside frequency, mean downside variation and downside magnitude. Downside frequency is expressed as a percentage of returns below MAR over the course of 100 months. So a downside frequency of 25% would mean that the asset class is going to return 25 months of under performance over 100 month time frame. Downside mean variation is the average size of the return below MAR and downside magnitude is the worst case return below MAR. Once we have calculated downside risk we can calculate the risk adjusted return for the portfolio. It is imperative at this point to ensure that asset classes selected for the portfolio have adjusted returns greater than MAR.

The below figure is a graphical representation of a positively skewed asset class, plotted against a normal distribution and the MAR.




2.2 POST MODERN PORTFOLIO THEORY CALCULATIONS




Access to fund price data is fairly impossible to obtain without paying a huge price and membership fees to buy data points. As a result, calculating Downside Deviation is almost impossible. However we have done the next best thing, which is to use inference based estimates for our portfolio. Our calculations gives a minimum return is around S$4.5m which we feel is already quite conservative and achievable while for Year 5, we are expecting a to end at S$1.66m.










To summarise, Mr. and Mrs. Lee could safely achieve their goals with minimum downside. By looking at the chart, the downside deviation (weighted in 80% equities, 10% bonds and 10% REITS) in Year 1 is an expected maximum of 0.12377 on every dollar.

For the 5 years downside deviation is a maximum of 0.27785 on a dollar, while the weighted expected mean value would be 1.66151816.

For every dollar invested, the expected minimum value (Weighted expected mean value less weighted CDD): -
Year 1 → 0.97992
Year 5 → 1.42701316
Year 15 → 4.58662782

To Sum it up, the maximum downside risks for Year 1 is likely to be 2.1% while from year 2 onwards, the portfolio is expected to have positive (nominal) returns. If the investor stays invested for the entire 15 years, One million could grow to 4.58 million, exceeding Mr. and Mrs. Lee's targeted minimum Accepted Returns of 9.68% with a very high degree of certainty.


NOTE:
** REITS assumed mean return = 5%.
Small stock is used as a Proxy for Small Capitalisation Value Stocks
Large Stock is used as a proxy for large value stocks
*REITs carry characteristics of Bonds while also behaves as an equity. In view of absense of data, we assume that the CDD of REITS will mirror 50% of the behaviour of Long term government bonds and 50% of Large stocks.