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The Parables of Investment

From an interesting paper:
The parables, premium puzzles, and the CAPM
by Hong-Jen Lin and David C. VanderLinden
image source

Rate of return, risk free deposit, and equity premium

In Matthew 25: 14-30 (the Parable of the Talents), a master has given his three servants five talents, two talents and one talent of money, respectively. The first earns five more talents, the second earns two more talents, and the third earns nothing since he played it safe and buried all the money in the ground. The master commends the first and the second ‘‘Well done, good and faithful servants’’ (verses 21 and 25) but excoriates the third as a ‘‘wicked, lazy servant’’ (v. 26).

A key principle to this parable is risk-taking. The first two servants were willing to place at risk the endowment given to them, but the third servant was ‘‘afraid.’’ As interpreted by most commentators, the parable is an exhortation to take risks in using one’s gifts for the kingdom of God. Jesus indicates a reward for those willing to take risk, and punishment for the one who was too fearful (risk-averse).

Perhaps, we can also infer how the master evaluates performance of the investments by three servants. Why did the first and second servants receive the same praise and rewards? Both took risk and, while the absolute value of income differed, they both earned the same rate of return. In this case (but not for the Parable of the Ten Minas), the master gave them the same rewards. Proverbs 3:14 (in the Old Testament) also alludes to return: ‘‘for she (wisdom) is more profitable than silver and yields better returns than gold.’’ The concept of return appears in both the Old Testament and the New Testament.

Regarding the third servant, the master criticized, ‘‘you should have put my money on deposit with the bankers, so that I would have received it back with interest’’ (v. 27). Given the comment, we can surmise that the risk-free deposit market existed in Jesus’ era. The third servant is despised because he has earned zero return in investment, under the riskfree rate. Therefore, one can interpret the verse to mean that the master measures performance not just based on the rate of return but on the return rate in excess of the risk-free interest rate. This conforms to the formula of the Sharpe-Lintner CAPM:

ri – rf = Bi ( rm – rf )

where ri is the rate of return for asset i, rf is the risk-free deposit interest rate, and rm is the market return. Bi denotes the systematic risk. Both sides of equation are returns in excess of the risk-free deposit rate. In other words, the measurement of performance of investments is based on the rate of return in excess of the risk-free deposit rate.

A similar concept is found in the Parable of the Ten Minas (Luke 19: 11-23). However, in this parable, each servant is given one mina. The first servant invests it and returns ten minas to his master; the second invest the mina to return five minas; a third servant hides his mina in the ground because he is ‘‘afraid.’’ In the Parable of Ten Minas, the master rewarded the faithful servants by giving them authorities to rule cities; the first over ten cities, the second over five. That is, the ‘‘payoff’’ in the Parable of Ten Minas is much more than that in the Parable of Talents (as is the return), but it is proportional to the returns of each servant. Again, the criticism of the third servant’s inaction is still sharp.

The scripture seems to encourage investors to earn as much as possible. The master criticized the third servant because of his laziness. The laziness is simply caused by his fear of taking risk (v. 25). Therefore, according to the Parable of Talents, Christians are motivated to invest and accumulate wealth to glorify God. It seems that Jesus appreciates people who dare to take risk and grasp profitable opportunities. This is consistent with Solomon’s exhortation to enter into risky trade and ‘‘cast your bread upon the waters, for after many days you will find it again’’ (Ecclesiastes 11: 1). Consistent with Weber’s propositions, it may be that the financial markets have been influenced at least indirectly by these principles. That is, religious teachings can change people’s mindset and then motivate them to invest and to fully utilize the financial resources they have. As a result, financial markets are formed, which increases general wealth. The prosperity of financial markets further inspires researchers in forming financial theories such as the CAPM. A possible relationship among the biblical teachings, financial markets, and financial theories is illustrated in Figure 1.

Avariant of the CAPM is the consumption CAPM, in which investors hold wealth to allow consumption. Thus, the expected return on an asset should be related to how the asset’s returns vary with consumption. Mehra and Prescott (1985) found that the historical equity risk premium (the rate of return on stocks over and above the return on a risk-free rate) was too high for ‘‘reasonable’’ levels of risk aversion. Termed the ‘‘equity premium puzzle,’’ this finding has stirred numerous unsuccessful attempts to explain the puzzle. One possibility is that investors have diverse preferences or beliefs (rather than those of a representative individual as usually assumed). In both the Parable of the Talents and the Ten Minas, one investor either was too risk-averse to invest or had different payoff expectations such that he was unwilling to invest. Perhaps these parables offer an avenue of explanation for the equity premium puzzle.

According to Benartzi and Thaler (1995), when investors are myopic-loss-averse, the return on equity must be large enough to attract them to buy stocks. We can also observe from the Parable of Talents that the third servant is myopic-loss-averse. In other words, the third servant ignores upcoming rewards he might earn. His fear of loss is much more than the joy of gain. Therefore, the equity premium is a must to draw investors like him to invest in risky assets.

One final note on equities is in order. Because the master strongly motivates the servants to invest by authorizing them to rule over cities (i.e. have ownership of productive assets), this kind of teaching could be viewed as encouraging Christian investors to hold equities, as the light shed by Weber (1930).

In the field of corporate finance, equity holders may pass up profitable (i.e. positive net present value) investments when debt holders may get most of the benefits of the projects. That is, equity holders may tend to under invest when they realize that their gains in the new projects are limited (see Grinblatt and Titman, 2002, p. 563). In the Parable of Talents, similarly, the third servant may think that the master will get most of benefits so he is reluctant to invest. Actually, he really under invests: invests into the ground!

To sum up, conceivably these parables could help to explain the equity premium puzzle in asset pricing and the under investment problem in corporate finance. Teachings based on the parables may shape the behavior of people especially when these biblical teachings have already become a part of the system in a country.

Optimising Portolio of ING PPS Funds

What is ING PPS (Private Portfolio Service) Funds?
Private Portfolio Service is a master trust administered by ING. It has been developed as both a series of unit trusts and a superannuation fund, representing a broad range of asset classes and fund managers.

Private Portfolio Service provides investors with the opportunity to diversify their portfolio, without the need to rebalance different investments across a number of fund managers and products.
Someone definitely has to do a quantitative research on these funds, right? What's the purpose? To find the best and optimised alocation of a portfolio of one's retirement plan or any investment plan.

Based on their daily/monthly historical prices, I calculated the daily/monthly log return of each PPS fund, Ln(P2) - Ln(P1) to show the continously compounded return.

I then calculated the mean and standard deviation of each fund and built the covariance matrix. Next, I calculated the portfolio mean and standard deviation.

Finally, using solver, the optimised allocation is found by assuming risk free rate 7%. Contact me to get the optimised allocation and the spreadsheet, if you're curious or just checking with your own calculation.

Please confirm if these annualised monthly means and standard deviations are close with your calculation for data ending 21 Jan 08.

PPS mean stdev
AggBal 7% 0.087
AsianEq 10% 0.159
AusEq 7% 0.126
Bal 5% 0.063
DivTrad 3% 0.041
EuroEq 6% 0.138
GlobOpp -1% 0.176
InterEq 5% 0.131
InterFix 3% 0.029
Mortg 1% 0.018
NZEq 5% 0.098
NZFixed 0% 0.021
PlatInter 1% 0.101
Prop 6% 0.080

Some notes

Sorry, I didn't use CAPM return in this calculation. No market index benchmark therefore no beta and risk premium to consult. :-)

This is an optimisation of a portfolio of optimised funds as a managed fund is a portfolio which is optimised regularly by its fund managers.

Putting into practice, some clients don't believe in this simulation. This is because the simulation is based on the daily prices and they don't concern this kind of time horizon.

For getting the best point of view, in my opinion, it is best simulated from monthly prices, not daily prices.

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Top 10 Indonesian Managed Funds (Reksa Dana)

"Reksa Dana or Reksadana" is an Indonesian term for managed funds. The total number of managed funds in Indonesia is 475. It's amazing! And, the highest real return is around 70%!! Seeing the high return of Indonesia market, who cares about standard deviation...

Fixed Income
Shares 58
Mixed 111
Money market 32
Protected 103
Index 1
Listed 2

TOP Performers as of 29 March 2008 (in %)

SHARES funds
(Rp) 30 days 1 year 1 year real
Makinta Mantap 3.713,76 -16.76 66.27 62.19
Fortis Ekuitas 9.005,18 -12.42 57.97 51.83
Pratama Saham 2.118,94 -13.2 52.08 50.57
Fortis Infrastruktur Plus 1.557,37 -11.64 54.2 49.29
Optima Saham 1.578,07 -8.16 53.57 48.3
Bahana Dana Prima 8.163,82 -12.05 51.93 47.44
Schroder Dana Istimewa 2.677,91 -8.53 46.77 46.04
Danareksa Mawar 4.715,90 -11.8 47.52 45.33
Mandiri Investa Atraktif 2.757,80 -13.65 46.86 45.21
Reksa Dana Dana Ekuitas Prima 2.320,73 -11.58 53.53 43.7

MIXED funds
(Rp) 30 days 1 year 1 year real
Prospera Balance 2.788,39 -11.37 59.5 53.25
Bahana Dana Infrastruktur 4.997,78 -11.91 56.33 51.71
Fortis Pesona 11.610,89 -11.24 50.22 46.87
TRIM Syariah Berimbang 1.441,77 -9.95 43.37 43.37
Mandiri Investa Syariah Berimbang 2.136,52 -4.25 44.52 41.65
Reksadana Mega Dana Syariah 1.533,92 -6.92 42.78 39.95
Star Balanced 1.778,10 -6.06 42.03 39.9
Danareksa Anggrek Fleksibel 1.895,27 -8.04 44.53 39.62
Schroder Dana Prestasi 12.447,40 -10.69 41.64 38.49
Mega Dana Campuran 1.538,57 -8.55 40.61 37.15

Which Market do you prefer?

"IHSG" is the Jakarta Market. Isn't it way too high? The mean and also the stdev.

"NZXall" is the the good one I think. It has a considerably high mean and low stdev.

US Recessions and the MSCI World Index

Recent market talks are around the fears of recession in the US. Although finance is often considered as sort of an exact science, it however cannot avoid the influence of the state of anxiousness by market players and investors. That is why a behavioral finance matters and needs to be neutralised by showing the real facts in the financial markets and a good sense to answer if a US recession is really going to bring down the entire world financial market in the long term.

Periods of US recession and the definition

The state of US recession period is officially announced by the National Bureau of Economic Research (NBER). Since 1970 there have been 5 states of recession in the US, as follows :
• November 1973 to March 1975
• January 1980 to July 1980
• July 1981 to November 1982
• July 1990 to March 1991
• March 2001 to November 2001

The NBER defines that
“A recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales. A recession begins just after the economy reaches a peak of activity and ends as the economy reaches its trough. Between trough and peak, the economy is in an expansion. Expansion is the normal state of the economy; most recessions are brief and they have been rare in recent decades.”

The informal recession definition is a decline in the Gross Domestic Product (GDP) for two or more consecutive quarters.

Relationship between recession and stock market decline

There is a confusing logic in relationship between recession and stock market decline: does a recession cause a bearish market or the other way around? The exact answer is that the recession comes first and the bearish market after. In a recession, analysts would see the value of companies is declining therefore the stock prices may fall. However, some classic strategy suggests that investment in the consumables sector may be a recession-proof investment since people still buy those products, recession or not.

If the recession comes first and the bearish market after, how can we explain the states of US recession in July 1990 to March 1991 that came 3 years after the 87 crash? Many analysts argue that the Crash was mainly caused by a programmed trading system and psychology factor that beyond the economic factor of an exact finance. The “quants” (quantitative traders) who developed a computerised trading system that automatically created a sequence of selling positions might had been to blame, or it could had been the investors who were psychology weak and then fell into selling positions.

How strong is US recession influence on global market?

Another question to answer: does US recession strongly influence the global financial market, particularly Australia and NZ markets? It may not be. Asian countries like Japan, China, South Korea and others have been the dominant trading partners for Australia and therefore NZ for the last decade competing trading flows with the US. This recent economic decoupling theory may explain how US recession may be absorbed by growth in the competing countries (Asia) as maintaining trading flows with the third trading counterparts (Australia/NZ).

Some simple examples: the US recession may not affect New Zealanders to stop buying stuff from the Warehouse stores, but Americans to visit their Walmart stores. New Zealanders are not going to disconnect their Telecom line at home because of the US recession.

The recent subprime trouble in the US economy may be likely to influence ASX and NZX in terms of market psychology rather than concluding a good excuse and common sense that Australian and NZ companies should decline in value because of it. The fundamental assessment of companies’ value seems to be flawed in the short term.

Unfortunately, the recent January big drop in Asian and European markets is however breaking the belief of the decoupling theory. Investors and market players are then more aware of the true impact of US recession on the global financial market.

Market randomness over recession period

It seems some finance and economics theories try to explain and justify the prediction of world’s share market trend in the future. However, contradictions, unpleasant facts and non-economic factors may affect one’s prediction and there is only one underlying theory that can explain all this, i.e. randomness and stochastic.

Therefore, it is important to show some historical fact to see the ex post impact of US recession to the world financial market by taking a closer look at the historical data of popular benchmark of the world financial market, the MSCI World Index. The goal is to conclude that randomness in the share markets may be likely to drive the prices up in the long term regardless recession.

The conclusion of this can be easily understood by paying attention to the following chart, which show the period of US recession and the MSCI World Index. The fact is, in the time frames of 10-15 years the US recessions seems to have been driving the ex post movement of the world share market up. Therefore, recession is not a measure of uncertainty in stock market. Or, is it just because the market randomness factor always win over the recession factor?

1977 to 1987: two recessions and 280% return

A decade before the stock market crash of 1988, and despite the two recession periods were defined in 1980 and 1982, the MSCI had been dramatically increased by 280% return.

1987 to 1997: one recession and 135% return

After all, the MSCI index still increased by 135% despite the 1991 US recession was occurred.

1997 to 2007: one recession and 92% return

Regardless the Technology Crash 2000-2002 and the “War on Terror”, and despite the 2002 US recession, the MSCI index still increased by 92%.

The best example of the MSCI Index Fund managed in NZ is AMP Investments' World Index Fund (WiNZ)