The Parables of Investment

Mar 31, 2008
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.


Anonymous Timothy said...

cool blog took me to the time where i can't dream of

Oct 15, 2010, 4:00:00 AM  

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