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individuals. In the same era, Muslims emphasized on collective values in their legalcommitment. He further uses a game theory approach to infer that individual valueforms a positive institutional structure in the business world. His hypothesis coincideswith the findings of Guiso et al. (2002) that Christianity facilitates economic growth.

All of them provide behavioral interpretations on how religion is associated withfinance and economics from cultural perspectives. None explores the cultural orreligious roots of modern financial theories. Therefore, section 3 is designed to dealwith the relationship between biblical principles and the CAPM.

In the asset pricing literature, the SharpeLintner CAPM cannot fully explain theequity premium puzzle, size premium puzzle, and value premium puzzle. Mehra andPrescott (1985) and Fama and French (2002) indicate that the difference between thereturn on S&P 500 and risk-free interest rate exceeds 5 per cent, which is more than thetheoretical risk premium in the SharpeLintner CAPM. This is called the equitypremium puzzle.

The size premium and value premium (i.e. ratio of book-to-market equity effect) arecaptured by numerous studies and summarized by Fama and French (1993). That is,

the equities with smaller market values or high book-to-market ratios outperform otherstocks in the rate of return. We have found biblical concepts that are related to thesethree premiums.

3. The parables, premium puzzles, and the CAPM3.1. Rate of return, risk free deposit, and equity premiumIn Matthew 25: 14-30 (the Parable of the Talents), a master has given his three servantsfive talents, two talents and one talent of money, respectively. The first earns five moretalents, the second earns two more talents, and the third earns nothing since he playedit safe and buried all the money in the ground. The master commends the first and thesecond Well done, good and faithful servants (verses 21 and 25) but excoriates thethird as a wicked, lazy servant (v. 26).

A key principle to this parable is risk-taking. The first two servants were willingto 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 inusing ones gifts for the kingdom of God. Jesus indicates a reward for those willing totake risk, and punishment for the one who was too fearful (risk-averse).

Perhaps, we can also infer how the master evaluates performance of the investmentsby three servants. Why did the first and second servants receive the same praise andrewards? Both took risk and, while the absolute value of income differed, they bothearned the same rate of return. In this case (but not for the Parable of the Ten Minas), themaster gave them the same rewards. Proverbs 3:14 (in the Old Testament) also alludes toreturn: 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 ondeposit with the bankers, so that I would have received it back with interest (v. 27). Giventhe comment, we can surmise that the risk-free deposit market existed in Jesus era. Thethird servant is despised because he has earned zero return in investment, under the risk-free rate. Therefore, one can interpret the verse to mean that the master measuresperformance not just based on the rate of return but on the return rate in excess of therisk-free interest rate. This conforms to the formula of the Sharpe-Lintner CAPM:

ri rf irm rf 1

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where riis the rate of return for asset i, rfis the risk-free deposit interest rate, and rm is themarket return. idenotes the systematic risk. Both sides of equation (1) are returns inexcess of the risk-free deposit rate. In other words, the measurement of performance ofinvestments 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 itand returns ten minas to his master; the second invest the mina to return five minas; athird servant hides his mina in the ground because he is afraid. In the Parable of TenMinas, the master rewarded the faithful servants by giving them authorities to rulecities; the first over ten cities, the second over five. That is, the payoff in the Parable ofTen Minas is much more than that in the Parable of Talents (as is the return), but it isproportional to the returns of each servant. Again, the criticism of the third servantsinaction is still sharp.

The scripture seems to encourage investors to earn as much as possible. The mastercriticized the third servant because of his laziness. The laziness is simply caused by hisfear 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 Jesusappreciates people who dare to take risk and grasp profitable opportunities. This isconsistent with Solomons exhortation to enter into risky trade and cast your breadupon the waters, for after many days you will find it again (Ecclesiastes 11: 1).Consistent with Webers propositions, it may be that the financial markets have beeninfluenced at least indirectly by these principles. That is, religious teachings can changepeoples mindset and then motivate them to invest and to fully utilize the financialresources they have. As a result, financial markets are formed, which increases generalwealth. The prosperity of financial markets further inspires researchers in formingfinancial theories such as the CAPM. A possible relationship among the biblicalteachings, financial markets, and financial theories is illustrated in Figure 1.

A variant of the CAPM is the consumption CAPM, in which investors hold wealth toallow consumption. Thus, the expected return on an asset should be related to how theassets returns vary with consumption. Mehra and Prescott (1985) found that thehistorical equity risk premium (the rate of return on stocks over and above the returnon a risk-free rate) was too high for reasonable levels of risk aversion. Termed theequity premium puzzle, this finding has stirred numerous unsuccessful attempts toexplain the puzzle. One possibility is that investors have diverse preferences or beliefs(rather than those of a representative individual as usually assumed). In both theParable of the Talents and the Ten Minas, one investor either was too risk-averse toinvest 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 alsoobserve from the Parable of Talents that the third servant is myopic-loss-averse. Inother words, the third servant ignores upcoming rewards he might earn. His fear of

Biblical

Teachings

Investors

Mindset

Investors

Behavior

Researchers

Mindset

Financial

Markets

Financial

Theories

Figure The conceptu

relationship betwefinancial theories a

biblical teachin

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loss is much more than the joy of gain. Therefore, the equity premium is a must to drawinvestors like him to invest in risky assets.

One final note on equities is in order. Because the master strongly motivates theservants 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 Christianinvestors to hold equities, as the light shed by Weber (1930).

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

To sum up, conceivably these parables could help to explain the equity premiumpuzzle 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.

3.2. Asset selection and the benchmark portfolioThe Bible says little about diversification, although Solomon recommends Giveportions to seven, yes to eight, for you do not know what disaster you may come uponthe land. (Ecclesiastes 11: 2) This verse seems to speak clearly of the risk-reductionsought in diversification. However, the parables do not discuss diversification. Instead,Matthew 13: 44 (the Parable of the Hidden Treasure) and Matthew 13: 45 (the Parable ofthe Pearl) focus on concentration of ones wealth. In the latter parable, a merchantlooked for fine pearls. He has found one of great value and sold everything he had tobuy it, that is, to invest all his wealth on the most valuable goods.

This pearl parable is analogous to the concept of optimization in finance. In otherwords, we need to find the investment with the maximal value. Based on this concept,we eventually are able to find one pearl in portfolio theory.

In the CAPM, along the capital market line, on the efficient frontier, only oneportfolio is chosen when the risk free deposit exists. There is no other portfolio else canprovide investors with higher return and lower risk (see Figure 2).

3.3. Beta and the two-state modelThe systematic risk beta coefficient depicts how the overall market trend affect thereturn of an individual asset. Although the scripture does not express the term

fr

The Benchmark Portfolio

Efficiency

Frontier

Return

Standard

Deviation

Figure 2.The tangent portfolio islike a pearl on theefficient frontier

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systematic risk, the concept of systematic risk exists throughout the Old Testament andNew Testament. For instance, Genesis 41-47 describes how a business cycle fluctuatedwith seven-years prosperity followed by seven years depression and the whole worldeconomy followed the same pattern (Campbellet al., 1997, p. 59). In 1 King 17: 1, 2, there

was no rain for several years and all people experienced the drought. In Revelation, thewhole world will encounter the upcoming disaster in future. Consequently, the concept ofsystematic risk in the CAPM coincides with the biblical point of view.

What is the meaning of the beta coefficient? The two-state model developed byBernardo and Ledoit (2000) and OConnor and Rozeff (2002a, b) offers a newexplanation of this. Gain and loss are two situations that most investors concern in thepractice of finance. Gain and loss provide a less complicated and more intuitiveapproach than the concept of mean and variance in the CAPM. This complies with thereal reaction and behavior of the investors in the asset market. Their gainlossfinancial model is more practical than the traditional CAPM when information fromthe markets is limited. The gainloss model requires the data for two states only whilethe empirical meanvariance analysis calls for a big data set.

OConnor and Rozeff (2002a, b) apply the gainloss model in the CAPM andfinancial modeling to corporate finance. In other words, they are able to incorporate thegainloss model in the CAPM. The gainloss model employs the gain/loss ratio tocapture risk and return in asset pricing. The gain/loss ratio is the expected gain overexpected loss, written asE(Gi)/E(Li)[2] for asseti, whereGandLare gain and loss, andE(.) is the expected value. It is straightforward to use the gainloss ratio to describe thepreference of an investor. For instance, a high gainloss ratio satisfies the investorsgiven the same risk. They also find that the gainloss ratio increases when theportfolio is diversified. Thus, the most diversified market portfolio possesses thehighest gainloss ratio among all different combination of assets investments. Whenthe asset market is at the equilibrium and no arbitrage opportunity exists, the gainloss ratio of the market portfolio is the highest. In other words, in the context of thegainloss theory, the beta coefficient in equation (1) CAPM can be re-written as[3]:

iECLim

ELm

ECGim

EGm 2

where m represents the benchmark portfolio, CLimis the co-loss and CGim is the co-gainfor assetiand the market portfolio. Because the market portfolio has the highest gainloss ratio, all other assets share part of the gain/loss of the market portfolio inproportion as the beta in equation (2). Please notice that the beta can be calculated byeither the share of co-gain [i.e. E(CGim)/E(Gm)] or the share of co-loss [E(CLim)/E(Lm)]since the two different calculations are identical in equilibrium. Consequently, the beta

coefficient is denoted by the ratio of the expected co-gain (co-loss) of asset iand thebenchmark portfolio (asset m) over the expected gain (loss) of the benchmark (asset m).By using the expected gain and loss to capture the systematic risk beta, the gainlossmodel dramatically simplifies the calculation of beta.

In the context of the two investment parables we discussed (Talents and Ten Minas),perhaps the lazy servant did not invest because he had a very high level of riskaversion or different expectations of the gain versus the loss. Similarly, Paul saysI consider the sufferings of this present time (expected loss) are not worthy to becompared with the glory that is to be revealed to us (expected gain). (Romans 8: 18)In fact, we could stretch a bit and assert that the Bible often presents a gainloss

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model: repent or perish (Luke 13: 3), evil or righteous, eternal punishment or eternallife. Therefore, the Parable of the Sheep and Goats (Matthew 25) discusses which wayis good and which way is not good. In parallel with the gainloss descriptions in theScripture, the gainloss model explains the behavior of investors in the practice of

finance and the implicit meaning of beta.Moreover, some cited that Bible verses capture the gainloss beta in equation (2). In

section 3.2, the benchmark portfolio is analogous to the pearl of great value, whichcaptures the kingdom of God. Thus, the co-gain (co-loss) of assets iand m is analogous tothe co-gain (co-loss) of an individual and the Lord; the expected gain (loss) of thebenchmark portfolio m is analogous to the expected gain (loss) of the Lord and theexpected gain (loss) of assetiis analogous to the expected gain (loss) of an individual.The gainloss beta [the expected co-gain (co-loss) of assets iandm over the expectedgain (loss) of asset m] also explains the share of asset i in the benchmark portfolio. InRoman 8: 17, Now if we are children, then we are heirsheirs of God and coheirswithChrist, if indeed wesharein his sufferings (i.e. co-loss) in order that we may alsosharein his glory (i.e. co-gain). Therefore, the gainloss beta reveals the expected co-gain

(co-loss) in proportion to the expected gain (loss) of the benchmark portfolio. The co-gainand co-loss reveal the gain and loss of individual asset ithat participates in gain and lossof the overall market portfolio. That is, the two-state beta describes the co-share of gainon asset iand benchmark in comparison with the gain on the benchmark only.

3.4. The size premium and value premiumThe small size stocks and high book-to-market ratio stocks usually earn higher returnsthan other stocks. These anomalies are called the size premium for small stocks andthe value premium for value stocks. Small stocks refer to firms with low marketcapitalizations and value stocks refer to high book-to-market ratio companies. Famaand French (1993) initiate the empirical study of the three-factor CAPM andincorporate the concepts of value and small stocks.

We find that the Bible seems to encourage investments in both value and smallassets. The size premium puzzle is revealed in the Parable of a Mustard Seed. Matthew13: 31 and Luke 13: 19 note that a small mustard seed can grow to a big tree. Theseparables point out the potential of a seed to grow. Therefore, the kingdom of God isgrowing like a mustard seed because the seed grows and the value of the seedmultiplies. The small mustard seed is analogous to the small stocks. Similarly, thevalue of a small company comes from its potential to grow. A mustard seed can growup to be thirty, sixty, and one hundred times as original size. When investors plantseeds in the small companies which they have faith in, the return on small-sizecompanies will be great.

In parallel with the size effect, value stocks earning more can be seen in the teaching

on the Parable of the Hidden Treasure. Both this parable and that of the pearl suggestthe importance of investing in the most valuable assets, which is analogous to theinvestments in the value stocks (i.e. high book-to-market ratio assets). In the Parableof the Hidden Treasure, a man sells all he has to buy a field with hidden treasure.Therefore, the value asset is acquired. The Parable of the Pearl describes the sameconcept. To sum up, we believe that the parables may give insight into the value stocksfactor and small size factor described in Fama and French (1993) and may suggest thethree-factor CAPM. That is,

ri rf 1irm rf 2iSB 3iH L 3

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where S is the return on the small size assets, Bis the return on the big size assets,Hdenotes the return of the high book-to-market portfolio and L represents that of thelow book-to-market portfolio, and1i, 2i, and 3iare the coefficients of the equation.This three-factor model considers both size effect and book-to-market ratio effect.

3.5. Summary of the parablesThis section mainly incorporates the parables in the New Testament into thediscussion on the CAPM. We illustrate the parables to cover several topics includingthe SharpeLintner CAPM, the gainloss beta, and the three-factor model.

Table I lists the parables in the Books of Gospels in relation with finance theories.The classification of parables is based on Dreyer (1952). We focus on the Book ofMatthew since Matthew quotes most parables on finance (9 out of 12). We have foundfour parables relating to finance in the Book of Mark. And in the Book of Luke, only 3out of 13 parables are associated with modern finance theories. This coincides with thefact that Matthew was a tax collector who may have expertise in finance. Interestingly,the Parable of Ten Minas is the only important parable in finance that is recorded in the

TableThe parables in t

Gospels associated wfinancial theor

Chapter Also seen in ModelPremiumpuzzles

Parables in MatthewThe Salt and Light 5 NA NA NAThe Lamp 5 Mark, Luke NA NAThe Sower 13 Mark, Luke NA NAThe Weeds 13 Mark Gainloss NAThe Mustard Seed 13 Mark CAPM (3) SizeThe Yeast 13 Mark CAPM (3) Size

The Hidden Treasure 13 NA CAPM (3) ValueThe Pearl 13 NA CAPM (3) ValueThe Net 13 NA Gainloss NATen Virgins 25 NA Gainloss NATalents 25 NA CAPM EquitySheep and Goats 25 Mark, Luke Gainloss NA

Parables in MarkThe Growing Seed 4 NA NA NAThe Tenants 12 Luke NA NA

Parables in LukeThe Good Samaritan 10 NA NA NAThe Great Banquet 14 NA NA NAThe Lost Sheep 15 NA NA NA

The Lost Coin 15 NA NA NAThe Lost Son 15 NA NA NAThe Shrewd Manager 16 NA NA NAThe Persistent Widow 18 NA NA NAThe Pharisee and the Tax Collector 18 NA Gainloss NATen Minas 19 NA CAPM Equity

Notes: CAPM, Sharpe (1964) and Lintner (1965) CAPM; CAPM (3), the three-factor CAPM of Famaand French 1993; gainloss, OConnor and Rozeff (2002a, b) the gainloss CAPM; NA, not available;equity, the equity premium puzzle; size, the size premium puzzle; and value, the value premium puzzle

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Book of Luke instead of the Book of Matthew. It is also the only parable in the Book ofLuke related to the SharpeLintner CAPM.

4. Conclusion

This study reviews parables and other Bible passages on investment rules. These rulesseem to be particularly relevant to the CAPM. Jesus parables on the kingdom of Godindicate prevailing terminologies and concepts in asset pricing.

The Parable of Talents and the Parable of Ten Minas discuss the concepts of the rateof return and risk-free deposits. They both encourage risk-taking investments thatentail the equity premium. And the Parable of the Pearl is associated with thebenchmark asset along the efficiency frontier and the value stock in the portfolio.It also fosters the value premium in asset pricing when the investors are influenced bythe biblical teachings. Furthermore, the Parable of the Mustard Seed highlights theimportance of investing in small companies, which implies the size premium.Moreover, the Parable of the Weeds and the whole Bible can be seen as a gainlossmodel to differentiate the two states, gain and loss. If you make a right decision, yougain. Otherwise, you lose.

The concept of the systematic risk is shown throughout the whole bible from theOld Testament to the New Testament. Diversification is prescribed by Solomon as ameans of reducing risk, but a concentration ones wealth on the hidden treasure (i.e. themarket portfolio) is encouraged in the parables. In addition, the gainloss model can beextended to the discussions in the Parable of Weeds. In this limited review of Biblicalanalogies, we see that the three-factor CAPM of equation (3) as consistent with theparables, and the gainloss beta [equation (2)] is associated with the duality in thescripture.

Parables in general can definitely contribute to finance education by makingcomplicated concepts easy to understand. Nevertheless, the parables do not differentiate

real investments from financial investments. As far as we know, the pattern of realinvestments is less volatile than that of financial investments. Moreover, the Bible seemsto discuss the fundamentals of investments rather than technical analysis. Hence, whileBiblical finance may cover only some aspects of financial theories, it is an essential partof finance and makes finance more meaningful and complete.

Notes

1. The monetary authorities can create demand for a new monetary unit by enforcingspaceship owners to hold it. Because people need spaceship travel, the demand for a newmonetary unit is created.

2. E(Gi) andE(Li) denotes the expected value in all states of gains and expected value of allstates of loss for asset i, The calculation of them are EGi

Ps:ris>rf

sris rf and

ELi P

s:ris>rf sris rf for state s and asset i. where s is the probability whenstate s takes place, ris represents the return on asset i in state s , and rf represents therisk-free interest rate.

3. E(CGim) denotes the expected value in all states when the market return exceeds therisk-free interest raterffor asset i, and E(CLim) denotes the expected value in all stateswhen the market return is lower than the risk-free interest rate rf for asset i,Algebraically, ECGim

Ps:rim>rf

sris rf and ECLim P

s:rms>rfsris rf

where s is the probability when state s takes place, ris represents the return on asseti in state s, rim represents the return on the benchmark portfolio in state s, and rfrepresents the risk-free interest rate.

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Corresponding authorHong-Jen Lin can be contacted at: linh@nyack.edu

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