Is it possible to reliably estimate the cost of capital with CAPM (or any other factor model)?

In a previous post I discussed why the cost of debt has little influence on investments. What about the cost of equity? Firms typically use (much) more equity than debt to finance their investments. So the cost of equity should matter more. In a recent study, Murray Frank and Tao Shen investigate how the cost of equity and the weighted average cost of capital (WACC) influence investments of US firms.  Remarkably, they find that the cost of equity and the WACC are positively related to corporate investments. Firms with a higher estimated cost of equity and WACC tend to invest significantly more. That is a very strange result. We would expect firms with a high cost of capital to invest less, not more.

Perhaps something is wrong with the model that Frank and Shen use to estimate the cost of equity? They focus on the Capital Asset Pricing Model (CAPM) which is still the most commonly used model for determining the cost of capital. In a recent survey of finance professionals, Lilia Mukhlynina and Kjell Nyborg find that 76% of these professionals use CAPM. Nevertheless, CAPM has been criticized a lot. The model assumes that the expected return on investments is determined by their systematic risk, i.e. the extent to which the return to the investment is correlated with overall market return. Researchers including Nobel price winner Eugene Fama argue that other factors such as market capitalization and the market-to-book ratio also affect the expected return of investments, up and above systematic risk. These factors should therefore be included in any empirical model that estimates the cost of equity. However, the findings of Frank and Shen not only hold for CAPM but also for the two most commonly used alternative factor models: the Fama and French three factor model and the Carhart version with four factors. Frank and Shen additionally check whether their results hold for different time periods, they take into account differences in firm size and leverage, add additional price factors, consider the possibility of autocorrelation which may affect their findings and use different estimation periods to determine the cost of equity. Whatever they do, the positive relation between the equity cost of capital and corporate investments remains significant. 

However, when they try a different approach to estimate the equity cost of capital, the implied cost of equity capital, the relation between cost of capital and corporate investments becomes negative. This is what we would expect: a lower cost of equity capital makes it cheaper to finance investments and hence induces firms to invest more. Calculation of the implied cost of equity capital is based on valuation models such as the Gordon growth model and the residual income model, which value equity by discounting expecting future cash flows or earnings. If you have estimates of equity value (based on the stock market price) and expected future cash flows or earnings (based on analyst forecasts), you can 'back out' the implied cost of equity capital. This is the cost of equity that stock market investors use to value the stocks (assuming that their expectations about future cash flows / earnings tend to be in line with those of analysts).

Why then is there a positive relation between factor model estimates of the cost of equity and corporate investments? From an economic point of view this does not make sense, and Frank and Shen are not able to explain the positive relation. Anyway, their findings raise serious doubts about the validity of factor models for determining the cost of capital. This is troubling, since these models still are the most common approach to estimate the cost of equity and WACC. The findings of Frank and Shen suggest that the implied cost of equity is a better approach. Unfortunately there are limits to this approach. Estimation requires not only the availability of stock market prices but also reliable estimates of expected future cash flows or earnings, which are often not available. A major advantage of CAPM is that it is a fairly easy model to estimate, which explains why it is still so popular with finance professionals.

Interest rates are very low: why don't firms invest more?

When interest rates are low, firms can borrow cheap, which lowers their cost of capital. It can therefore be expected that firms invest more when interest rates are down, since they will have more projects for which the expected return is higher than the cost of the capital. However, while interest rates have been at historically low levels in recent years, the effect on investments seems to be very limited. Why is that?

First, firms not only fund their investments with interest paying debt but also with equity. The overall cost of capital is the weighted average of the cost of debt (i.e. the interest rate, taking into account the tax deductibility of interest payments) and the cost of equity. Firms typically use (much) more equity than debt to fund their investments. The cost of equity is substantially higher than the cost of debt, because the cost of equity includes an risk premium that compensates investors for the volatility of equity returns. This equity risk premium is not fixed but varies over time. As a result, the cost of equity, and therefore also the weighted average cost of capital (WACC), is not closely tied to current market interest rates. This weakens the relation between interest rates and investments.

Second, when firms decide about an investment project, they often use a hurdle rate that is much higher than the estimated cost of capital. In a survey of US firms, Jagannathan and colleagues find an average hurdle rate of 15%, while the average WACC of these firms is only 8%. The hurdle rate also tends to be stable over time and firms care little about changes in interest rates. One reason why firms use such a high hurdle rate could be that they are financially constrained. That is, they cannot find enough funding to finance all valuable projects. As a result, they have to restrict themselves to the projects with the highest returns. However, Jagannathan et al. find that financially constrained firms actually use hurdle rates which are closer to their cost of financial capital, while firms with ample financial flexibility in the form of low debt ratios and high cash balances use higher hurdle rates. Their results suggest that it is nonfinancial, operational constraints, such as managerial or organizational requirements, that make firms more selective in making investments.

Interestingly, they also find that hurdle rates reflect idiosyncratic risk, i.e risk that is specific to individual firms. For example, the CEO of the firm might unexpectedly die, which could have large consequences for the firm, but matters little or nothing for the rest of the economy. According to standard portfolio theory, idiosyncratic risk does not affect investors who hold a diversified portfolio. If your portfolio consists of many different securities, the idiosyncratic risk of the different securities will cancel out if your portfolio is large enough. As a result, investors do not have to be compensated for idiosyncratic risk, and this risk should not affect the cost of equity. However, if the firm’s shareholders are not well-diversified, it makes sense to add a premium for idiosyncratic risk in the hurdle rate for investments: the shareholders need to be compensated for idiosyncratic risk that they cannot diversify away. Actually, many firms are controlled by shareholders which are not well diversified. Most firms are not listed on a stock exchange, and non-listed firms typically have a limited number of shareholders who have a substantial part of their wealth invested in an equity stake that they cannot easily sell. Even many (actually most) listed firms around the world are controlled by shareholders who have a substantial stake invested in the company. Idiosyncratic risk matters for those shareholders, and it makes sense to take it into account when setting the hurdle rate for new investment projects.

Finally, the value of investments not only depends on the required rate of return, but also on the expected return of investment projects. If there are fewer good investment opportunities in times when interest rates are low, firms in the aggregate will invest less even if it is apparently cheap to invest. So, the current lack of investments may also reflect a (perceived) lack of good investments opportunities.

Economic myths I: the European convergence myth

Politicians and people employed by European institutions often argue that we should have further economic, fiscal and financial integration in the European Union. They claim that this would inevitably lead to economic convergence between its member states, allowing poorer member states to catch up with the richer member states. As the European Commision puts it in a recent report: 'A complete EMU is not an end in itself. It is a means to create a better and fairer life for all citizens, to prepare the Union for future global challenges and to enable each of its members to prosper'. And according to European Commission President Juncker, 'the time has come to deepen European integration instead of re-introducing national divisions'.

This all sounds pretty good, but is it true? Will further integration really lead to convergence? To answer this question, it is interesting to take a look at the history of Italy. Italy was unified in 1861, but it has always been a diverse country. In a recent study, Emanuele Felice from the Autonomous University of Barcelona investigates the evolution of regional income inequality in Italy since its unification in 1861. He considers relative per capita GDP in Italian regions in the first year of each decade, from 1871 to 2001. Instead of economic convergence, he finds a tendency towards economic divergence in the Italian union since 1871: regional economic inequality has substantially increased over the past 150 years. In 1871, per capita GDP in the Southern regions in Italy was 90% of overall per capita GDP in Italy, while that of North-Western regions was 114% of overall per capita GDP. By 2001, relative per capita GDP in the South had declined to 68% (!), while that in the North-Western regions had increased to 124%. The decline in the South was especially pronounced after the first World War. Felice also finds a divergence when he considers the per capita GDP of 20 individual Italian regions. One striking example is Sicily, which went from 95% in 1891 down to 58% in 1951 and 66% in 2001. While the reasons for increasing regional income inequality after Italian unification are not clear, these findings demonstrate that it is simply not true that economic, fiscal and financial integration inevitably leads to economic convergence. The Italian case suggests that European unification could very well increase regional inequalities within Europe.

Regrets suck

Home sweet home

Never underestimate the creativity of the financial industry when it comes to finding new ways to repackage risk and returns. Recently, an American start-up called point.com has provided a new way to finance your home. Their slogan: Regrets suck so let’s avoid them. The basic idea is as follows. Point.com buys an “equity stake” in your home, you can use the money they pay for whatever you want, and you don’t have to pay any interest. Isn't that great? When the contract ends after a predetermined number of years, you pay back the equity stake, interest free. If the value of your home has gone up, you additionally pay a percentage of the home’s value appreciation.

For example, it could work like this. You sell a 10% equity stake in your home which is valued at $ 200,000, in exchange for 20% of the home's appreciation. This means you get $ 20,000 from point.com, which you have to pay back at the end of the contract. Let’s assume the estimated value of your house will then have gone up to $ 300,000. You pay back the original $ 20,000 plus 20% of ($ 300,000 - $ 200,000), i.e. the share of point.com in the value appreciation of your house. The total amount you pay to point.com is therefore $ 40,000. If your house has gone down in value by that time, you only pay $ 20,000. According to the point.com website, you can cancel your contract and pay back at any time before the agreed term.

This is definitely a very smart idea. Not surprisingly, point.com is backed up by an impressive list of investors including Andreessen Horowitz, one of the most prestigious VC-firms in Silicon Valley (*). However it is also a dangerous idea. If this new way of financing homes takes off, it is going to create a lot of trouble. First, the use of the term “equity” is very misleading. Point.com don't buy an equity stake in your home. Rather, they give you a loan (without interest) which you have to pay back. In return for not having to pay interest you give point.com a call option on the value of your home. If the home value goes up, point.com get a significant share of the appreciation. Basically, you sell a convertible loan to point.com. They are actually rather vague about how high the share they get will be. The only indication I found on their website was an example, in which the home owner has to give 20% of value appreciation in case of a 10% equity stake. This call option implies that the higher the value of your house, the more you have to pay to point.com.  If you’re cash strapped, it is therefore likely that you will have to sell your house, unless you have become substantially richer by the time you have to repay point.com. But if the value of the home goes down, you might also be in trouble. Point.com always gets the full amount of their loan back. If you have borrowed $ 20,000 from point.com and the value of your house declines from $ 200,000 to $ 150,000, you still need to pay back the full amount of $ 20,000 to point.com. If you don't have that money, you will be forced to sell your house at a substantial loss.

From a macro point of view, this seems like a new “trick” to make money out of people who can't afford to buy a house and will have to sell their home when the loan expires. It creates the illusion that you don't borrow: you don’t have to pay any interest! But in the end, you always pay.

(*) I recommend Marc Andreessen on Twitter; Ben Horowitz has written an interesting book on start-ups: these are very smart guys.