# Financial Modeling – Utilities & Other Industries Essay Sample

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1. The Capital Asset Pricing Model (CAPM) is a model used to compute the required rate of return of a specific investment. This required rate of return is also referred to as the cost of capital. The CAPM allows to compute a risk-adjusted rate of return, meaning that it takes into account the standard deviation of a stock price into the calculation, consistent with the fact that taking more risk should yield higher returns. The determinants of the required return are the market required rate of return, the risk-free rate and the beta (which measures the correlation of the stock price with the broader market). Said another way, the CAPM prices risk into investors’ expected return. The CAPM is – as every financial model – a way to simplify complex markets and phenomena. To do so, Sharpe (1964) and Lintner (1965) discussed in their papers the assumptions that accompany this theoretical framework. They refer to the security markets and to the market participants:

## Security markets are perfectly competitive.

Security markets’ transactions encounter no frictions – which means no transaction costs, no taxes, no illiquidity

All market participants have homogeneous expectations (Hillier et al 2010) – i.e. same investment horizon and return expectations

## All market participants have perfect information and equal access to it

All markets participants are price-takers

All markets participants are rational mean-variance optimizers – in other words given a certain investment return they will choose the one with the lowest risk

## Finally, unlimited borrowing can be done at the risk-free rate of return.

2. As can be seen, the following assumptions are simplifications of the real world and therefore do not always apply. For instance, the assumptions that security markets encounter no frictions is debatable. Although some types of deferred taxes account exist to trade shares in some jurisdictions, most market participants engaging in a transaction will be affected by taxes. Secondly, brokers do charge transaction costs for executing trades on behalf of their clients. Finally, illiquidity is likely not an issue if investing in large-cap stocks, although it is for investors wishing to trade small-cap shares. Other assumptions also seem to bear little resemblance with the underlying reality of most financial markets: the idea that all investors have homogeneous expectations and the same time horizon is hard to justify – how could it be the case when financial markets are used by people in all stages of life with very different needs, consider for instance the preference for current income over long-term growth?. Furthermore, Fama and French (2004) declared themselves that “unrestricted risk-free borrowing and lending is an unrealistic assumption”. While having pointed out some discrepancies between some of the CAPM assumptions and the reality, we should also point out that some assumptions are very relevant. Consider for instance the assumption that “All markets participants are rational mean-variance optimizers”. Why would an investor bear more risk than is needed on a certain expected return? Hence, this assumption of the CAPM seems to accurately model the psychology of the vast majority of market participants.

The fact that some of the CAPM assumptions are invalid in practice does not entirely render this model inapplicable. While demonstrating little empirical validity, the CAPM provides a useful model to calculate expected returns and take into account specific security risk – as proxied by beta. The underlying message of the CAPM is sound: more risk should translate into higher expected returns – and the model provides a systematic mathematical approach to this conundrum. Finally, the CAPM has been built upon to generate more advanced financial models known as multifactor models. These models use many determinants of expected returns – this compares to the CAPM which uses only beta. A famous model is the Fama-French 3-factor model used later in this paper.

3. I now proceed to do an empirical test of the capital asset pricing model using the following excess return models:

Rpt- Rft= α+ β*Rmt- Rft+ εt

I test the following hypothesis:

H0 :α=0

The two industries tested are the “Utilities” industry and the ”Others” industry. The first regressions concern both industries over the 30-year period for which results can be found in Appendix 1 and 2. Then these regressions for the two industries are repeated but the 30-year period is divided into three 10-year periods, for which results can be found in Appendix 3, 4, 5, 6, 7 and 8.

The utilities industry regression for the 30 year period gives us an intercept (alpha) of .49, and this value is statistically significant at the 1% level (p-value is <.01). This thus signifies that this industry generated positive abnormal returns over the period 1980-2010. The beta coefficient is 0.45 and is statistically significant at the 1% level (p-value<.01). A beta smaller than 1 means that the standard deviation of the returns are smaller than the market; in other words, the utilities sector was less risky than the overall market. Finally, the goodness of fit of the regression is relatively weak since the R Square has a value of .36, meaning that only 36% of the changes in the dependent variable is explained by the variation of the independent variable. When looking at the utilities industry regressions done every decade (Appendices 3, 4 and 5), we notice an intercept of .56 for the period 1980-1990, highly statistically significant (p-value<.01) and a beta of .50 also highly statistically significant (p-value<.01). We can say that during this period the utilities industry generated positive abnormal returns versus the markets – i.e. it was a great investment. For the 1990-2000 period, interestingly the alpha generated of .20 is not statistically significant (p-value>.39) and the beta of .35 is highly significant (p-value<.01). Therefore, while the industry was less risky than the overall market to a large extent (beta .35 versus 1), it also failed to generated abnormal returns. For the period 2000-2010, the intercept is the highest of the overall sample with a value of .78, statistically significant at the 5% level (.01<p-value<.05). This was done with a beta of .47 – statistically significant at the 1% level – proving that this alpha was obtained with less than commensurate risk. To conclude about the utilities industry, it was a satisfactory investment overall because of the positive alpha generated and the less-than-average risk. Because the results are statistically significant, we can reject the null-hypothesis in favor of the alternative hypothesis. When taking a look at the decades separately, the highest alpha was generated in the 2000-2010 period and the lowest risk was during the 1980-1990 period. These empirical findings are in contradiction with the CAPM, which states that superior investment returns (alpha) must come at the expense of greater risk. Empirically, our findings about the utilities industry over the sample period contradict this theory.

The “others” industry regression for the 30 year period gives us an intercept (alpha) of .20, but this value is not statistically significant (p-value>.19). Because the result is not statistically significant we cannot infer that the industry generated abnormal returns over the 30-year sample period. The beta coefficient is .87 and is statistically significant at the 1% level (p-value<.01). A beta smaller than 1 means that the standard deviation of the returns are smaller than the market; in other words, the “others” industry was less risky than the overall market – its risk was 87% of that which the overall market experienced. Finally, the goodness of fit of the regression is relatively weak since the R Square has a value of .66, meaning that only 66% of the changes in the dependent variable can be explained by the changes in the independent variable. We note that although this is notably better than for the utilities industry, it is not a satisfactory number. When looking at the “others” industry regressions done every decade (Appendices 6, 7 and 8), we notice an intercept of -.05 for the period 1980-1990, but this value is not statistically significant (p-value>.82) and a beta of .96 which is highly statistically significant (p-value<.01). We can say that during this period the “others” industry experienced slightly less risk than the broader market but we cannot conclude about the alpha. For the 1980-1990 period, the alpha generated of .10 is not statistically significant (p-value>.75) and the beta of .78 is highly significant (p-value<.01). Therefore, while the industry was less risky than the overall market (beta .78 versus 1), we cannot infirm that it generated abnormal returns once again. For the period 2000-2010, the intercept is the highest of the overall sample with a value of .59, statistically significant at the 5% level (.01<p-value<.05). This was done with a beta of .87 – statistically significant at the 1% level – proving that the industry experienced under-average risk. To conclude about the “others” industry, it was overall a less risky investment that the overall market (just like the utilities industry) but we cannot reject the null hypothesis and conclude that it generated abnormal returns because our results are not statistically significant. When taking a look at the decades separately, the industry did generate positive alpha in the 2000-2010 period (which was also the highest alpha for the utilities industry) and the lowest risk was during the 1990-2000 period. Except for the last decade, these empirical findings are in accordance with the CAPM, because we cannot infer that alpha was different from 0 – which is a requirement for the CAPM model to be valid. Empirically, our findings about the “others” industry differ from our findings about the “utilities” industry with the given sample.

4. After the shortcomings of the capital asset pricing model were highlighted by the financial community, Fama and French developed a three-factor model in 1992. This model builds upon the CAPM of William Sharpe as it uses not only one, but rather three determinants of returns in its equation:

## Mkt – RF, the market risk premium, which is used in the CAPM

SMB (Small Minus Big), which represent the excess return generated by small cap stocks compared to large cap stocks. This allows adjusting for the tendency of small cap equities to outperform large cap equities over time

HML (High Minus Low), which represents the excess return generated by stocks of high book-to-market ratio versus low book-to-market ratio. This allows adjusting for the fact the cheap stocks on a price-to-book ratio outperform expensive stocks on a price-to-book ratio over time.

The three-factor model is interesting and has a higher validity than the original CAPM model because it can account for up to 95% of the returns for the equity portfolios of all market capitalization (Ross 2012).

5. . I now proceed to do an empirical test of the capital asset pricing model using the following excess return models:

Rpt- Rft= α+ βpt*Rmt- Rft+spt*SMBt+hpt*HMLt+

I test the following hypotheses:

H0 : α=0 , H0 : β=0 , H0 : s=0 , H0 :h=0

The two industries tested are still the “Utilities” industry and the ”Others” industry. This time the regressions are only done for the full 30-year sample period and can be found in Appendix 9 and 10.

The multifactor regression for the Utilities industry has an adjusted R square is .52, which means that the independent variables (Mkt-RF, SMB, HML) explain 52% of the variations of the dependent variable. This is considered to be a relatively weak explanatory power, however this result is better than the .36 R square obtained with the CAPM model, thus correlating the findings of Ross (2012). The intercept (alpha) is .25 which is statistically significant at the 5% level (.01<p-value<.05). We can thus confirm that the utilities industry did generated positive abnormal over the sample period. Mkt-RF has a beta of .57 and HML has a factor loading of .47, both statistically significant at the 1% level (p-values<.01). Finally, SMB has a factor loading of 0, not statistically significant (p-value>.98). The beta suggests – as with the CAPM regression – that the utilities industry was less risky than the market. The positive HML factor indicates that some of the returns generated were due to buying value stocks (defined as high book-to-market ratios) since the expected returns have a positive correlation with HML. Since the SMB factor loading is not statistically significant, we cannot reject the null hypothesis and therefore cannot conclude about the impact of the size effect over the overall returns.

The multifactor regression for the “others” industry has an adjusted R square is .83, which means that the independent variables (Mkt-RF, SMB, HML) explain 83% of the variations of the dependent variable. This is considered to be good fit for the model, and we note that this result is better than the .66 R square obtained with the CAPM model, thus correlating the findings of Ross (2012). The intercept (alpha) is -.08 but it is not statistically significant (p-value>.45). We thus cannot infer that the “others” industry generated positive abnormal over the sample period. Mkt-RF has a beta of .91, HML has a factor loading of .49 and SMB has a factor loading of .63, all statistically significant at the 1% level (p-values<.01). The beta suggests – as with the CAPM regression – that the “others” industry was less risky than the overall market. The positive HML factor indicates that some of the returns generated were due to buying value stocks (defined as high book-to-market ratios) since the expected returns have a positive correlation with HML. The positive SMB indicates that some of the returns generated were due to buying small cap equities rather than large cap equities.

A noticeable result obtained by comparing the CAPM and Fama-French models is that the Fama-French regressions have higher R squares. Intuitively makes sense because determinants were considered to explain the dependent variable. Since the beta is not the only determinant of stock returns, the Fama-French model shows better results in explaining investment returns than the CAPM alone. The regressions for the “others’ industry are consistent with the financial theory because no alpha was generated over the full sample period, however results for the “utilities” industry did show abnormal returns being generated. This can either be interpreted saying that the theory does not work in this real world concept, or that some risk inherent to investing in the utilities industry is not captured by the three factors determined by Fama-French. Finally, we can conclude that Fama-French model is superior to the CAPM model in the sense that it carries a better predictive power than the CAPM of William Sharpe.

## References

Fama, E. F. and French, K. R. 2004. The capital asset pricing model: theory and evidence. Journal of Economic Perspectives, pp. 25--46.

Hillier, DJ, Ross, SA, Westerfield, RW, Jaffe, J & Jordan, BD 2010, Corporate finance: 1st European edition. Maidenhead.

Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics, pp. 13--37.

Ross, S 2012, “The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory, vol. 13, pp. 76-89.

Sharpe, W. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19 (3), pp. 425--442.

Appendices

Appendix 1 – Utilities – 1980-2010

Appendix 2 – Others – 1980-2010

Appendix 3 – Utilities – 1980-1990

Appendix 4 – Utilities – 1990-2000

Appendix 5 – Utilities – 2000-2010

Appendix 6 – Others – 1980-1990

Appendix 7 – Others – 1990-2000

Appendix 8 – Others – 2000-2010

Appendix 9 – Utilities – Fama French 1980-2010

Appendix 10 – Others – Fama French 1980-2010

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