Are we pricing private equity risk properly?


Financier Worldwide Magazine

July 2017 Issue

Investment is a double-sided coin of risk and return. Quantifying risk is, therefore, integral in estimating expected returns. Finance theory tells us that the value of any stock, bond or business is a function of its cash flows, discounted at an appropriate discount rate. For equity investors, the cost of equity is the expected return they need to make in the long term to compensate the risk that they have taken by investing. But is this risk being appropriately calculated for private equity investments?

Most theory based models define risk as both upside or downside variance over expected returns. Or in Mandarin: danger and opportunity. This risk is generally measured through the lens of the so-called ‘marginal’ investor in equity (and not the ‘average’ investor). This point is key. The marginal investor, i.e., the profile of the next pound or dollar in capital raised, is not only an investor who owns a large portion of the equity and trades frequently but is well diversified and has access to the ‘market portfolio’ (a theoretical weighted bundle of all available assets).

For private equity investments – by which we mean the broader universe of non-publically tradable asset classes – that is often not the case. For the owners of small businesses and startups, not only do ‘family, friends and fools’ (the first in line for financing requests) often invest most of their capital in their projects and companies – the equivalent of going ‘all in’ in poker – but early stage investors like angels and smaller VC funds may also not be fully diversified. Think of the entrepreneur who has invested all his savings in his new restaurant or the angel investor who cashed in his ISA to invest in a new tech startup. In a nutshell, that means that all risk – both systematic and non-systematic – is on the table.

In the traditional discounted cash flow (DCF) approach to valuation, the most widely used model to estimate risk and return in equity is the capital asset pricing model (CAPM). Notwithstanding (extensive) critiques, due to its simplicity and utility, it is still the workhorse of the professional 50 years after it was envisaged by William Sharpe, who would later go on to win the Nobel Prize in economics for the innovation. According to an Association for Financial Professionals (AFP) study, around 90 percent of the respondents use the CAPM to estimate their cost of equity.

In the CAPM universe, risk is broken down into market or systematic risk – measured by beta – which cannot be diversified away and non-systematic risk specific to the investment. Modern portfolio theory shows how specific risk can be mitigated through diversification. Therefore, a security’s expected return relies solely on its beta – its relationship to the overall market – and as most market professionals know is computed as a risk free rate plus the beta (the systematic risk factor), multiplied by a premium for equity risk.

Now, the idea of this article is not to simply restate basic finance theory but to pose a question extremely pertinent to investment valuation: if the private firm’s owner or an incoming investor does not have an opportunity to diversify, could the betas used to calculate expected returns understate the exposure to market risk in these companies? In other words, private equity valuations of economic value could be being overestimated. For professionals that depend on CAPM to estimate discount rates for private assets that could be an issue because assumptions about the costs of equity and debt, overall and for individual projects, and expectations around NPVs and return profiles, fundamentally impact investment decisions and resource allocation.

Total beta – a solution?

The beta of a company measures how the company’s equity market value changes with the change of market overall. By definition, private assets are not publicly traded, which means that we cannot ordinarily isolate the slope coefficient of the security’s price movement with the market. Therefore, we would use accounting earnings regressions, fundamental regressions or public sector averages (adjusted for financial leverage) to estimate an appropriate beta for the private asset, again assuming that the marginal investor is diversified. To bring into play the potential lack of diversification, and therefore systematic risk, there is a simple adjustment we can make to the beta formula.

Total beta, a concept introduced by the global authority on valuation, Professor Damodaran, and formalised by other practitioners, is a measure used to determine the risk of a standalone asset, as opposed to an additional asset added to a well-diversified portfolio. According to Professor Damodaran, to measure exposure to total risk, we can divide the market beta by the correlation of the private equity asset against the market index. The lower this correlation is, the higher the total beta.

The key point to bear in mind here is to define who the marginal investor in the private company or project is, and adjust the correlation with the ‘market portfolio’ accordingly. For business owners without any diversification at all, we can utilise the sector’s ‘full’ correlation coefficient. However, for buyers and investors with greater degrees of diversification, we can adjust the correlation upwards. Essentially, more diversification results in a higher correlation and by extension a smaller total beta modification. As such, if a private asset is to be acquired by a public company, no such adjustment would therefore be required. The profile of the marginal investor is also dynamic over time.

It is worth highlighting that the concept of ‘total beta’ is polemical in the valuation profession. Indeed, one commentator called a debate on the subject held at the American Society of Appraisers (ASA) a few years ago the “battle of the beta” due to the heated arguments between proponents and critics of the approach.

The main critique of total beta – and the total cost of equity (TCOE) which it computes – is that it violates the CAPM and by extension the broader Markowitz framework. The argument, put forward by Larry Kasper CPA CVA, is that modern portfolio theory dictates that all investors are mean-variance efficient. Therefore, these investors diversify and develop portfolios that plot on the Markowitz Efficient Frontier and they should thus price individual risky assets on the basis of the economic relationships that exist on the capital market line (CML). However, for private standalone assets the pricing model from the CML cannot simplify to total beta, but remains beta, unless the correlation coefficient of the security and the market is 1.0 (i.e., perfect correlation). Accordingly, beta is the relevant risk metric within the context of modern portfolio theory because it quantifies the amount of risk that will actually contribute to the risk of the portfolio that investors hold on the CML. If investors priced individual risky assets using any metric other than beta (such as total beta), then these securities, by definition, would be incorrectly priced unless their correlation coefficient with the market portfolio was equal to 1.0. There is also no empirical proof to back up the assumption that total beta definitely compensates investors for any lack of diversification.

Advocates of the approach argue that TCOE is a robust and widely used framework and it is in any case acceptable to violate the CAPM when valuing private firms for an undiversified investor. Moreover, is it any different from modified and built up CAPM models that include sector, country and size premiums? According to Butler, “After all, the mere presence of privately held firms violates the CAPM. CAPM calls for investors to hold the market (a completely diversified) portfolio. If most eggs are in one basket (one private company), the buyer’s portfolio will be dominated by the private company—thus, he or she is not holding the market portfolio, by definition”.

Moving away from the theory, if we simulate the calculation of a cost of capital using total beta against traditional beta, this can result in potentially significant deltas in economic value estimates.

Such results should be of interest for PE investors who price investments using internal rates of return and multiples of invested capital. According to a Harvard Business Review study, the vast majority of US based PE firms target returns of 20-25 percent, which are traditionally seen as being above CAPM-based rates. Considering the potential for higher TCOEs mapped out in this example, should this threshold be re-evaluated?

Adjusting our private equity discount rates for the lack of investment diversification not only makes intuitive sense but it does seem a more realistic alternative (with certain conditions) for valuation modelling, if obviously not a panacea for all potential risk on the table when dealing with privately held assets. We can assume that it works as well as the next best alternative in most cases (just like CAPM). The debate is likely to go on. This should not be surprising, there is, after all, very little consensus within the valuation professional even on basic assumptions, such as risk free rates and equity premiums. Appraisers should be mindful of the pros and cons involved in adjusting traditional costs of equity. Nonetheless, at the very least total beta provides an insightful framework to ideate around PE valuations and risk.

Nonetheless, let us recall some wise words from Warren Buffet: “Employing data bases and statistical skills, academics compute with precision the ‘beta’ of a stock – its relative volatility in the past – and then build arcane investment and capital-allocation theories around this calculation. In their hunger for a single statistic to measure risk, however, they forget a fundamental principle: it is better to be approximately right than precisely wrong...”


Adam Paul Patterson is a partner at ALFA Valuation & Advisory. He can be contacted on +55 41 99107 0765 or by email:

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Adam Paul Patterson

ALFA Valuation & Advisory

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