April 15, 2015
1) Background & Introduction To Time Diversification
In his recent article, What Practitioners Need to Know…About Time Diversification , Mr. Kritzman offers a comprehensive view on time diversification. As an example, Mr. Kritzman outlines the following:
Suppose you plan to purchase a new home in three months, at which time you will be required to pay $100,000 in cash. Assuming you have the necessary funds, would you be more inclined to invest in a riskless asset such as a Treasury bill or in a risky asset such as an S&P 500 index fund? Now consider a second question. Suppose you plan to purchase a new home 10 years from now, and you currently have $100,000 to apply toward the purchase of this home. How would you invest in these funds, given the choice between a riskless investment and a risky investment? (Kritzman, Page 29)
For the second question, Mr. Kritzman hypothecates that a typical investor would select a riskier asset for a longer term horizon as higher returns from the risky investment over longer period. In essence, the typical investor in the example above rationalizes the riskier investment choice due to the longer time period. At its core, that is what time diversification is about. It is the notion that above-average returns tend to offset below-average returns over long horizons.
However, Mr. Kritzman points out that several notable financial economists have argued the notion of time diversification is flawed. The primary reason being that while the annualized dispersion of returns converges toward the expected return over time, the terminal wealth in contrast diverges over time. That is, the magnitude of the losses actually increase with the passage of time as illustrated by the table below.
Source: What Practitioners Need to Know…About Time Diversification 1
As a professional in corporate finance, I believe Mr. Kritman’s insights on time diversification provides valuable cross application in the corporate finance world.
2) Time Diversification & Capital Allocation In Corporate Finance Context
As with the example provided by Mr. Kritzman, suppose you have $1 million in capital in engineering set aside for one of two options:
i) Alpha release,
ii) Beta release, and
iii) General Acceptance.
From a classical corporate finance perspective, based on the information in Table 2 and Table 3 below, one should be indifferent between Option A and Option B as the returns (Return (W)) are equivalent. However, from a utility and time diversification standpoint, the perceived value can be materially different. Observations below:
Observation 1: Time Influences Utility Curve & Therefore Capital Allocation Decisions
While this observation may seem like a Principal-Agent issue – it isn’t, again recall, the Return (W) is constant between Table 2 and Table 3. Rather, it focuses on perception of risk and the associated benefit over time. For example, incentive structures for management teams that tend to focus on equity and large value creation over time may cause them to take an aggressive position towards maximizing value at Year 3. Accordingly, the management utility curve may be expressed as an exponential function of the returns e ^ [Return(W)/1000] . In contrast, uncertainty in economic conditions may cause investors to be more risk averse and rely on a “certainty” in value creation by simply investing in the existing product. Accordingly, their utility function may be expressed as an inverse Utility curve -1/[Return(W)/1000] .
Based on the assumptions on the Utility Curve noted above, investors would have an increase in their utility for Option A, and a decrease in their utility with Option B, thereby compelling the risk-averse investors to accept Option A: Existing Product Development (see Table 4). In contrast, management would select Option B: New Product Development (see Table 5) as their utility increases with time.
Observation 2: If a Stakeholder believes they can alter results with Time, it will affect Capital Allocation behavior
In the Options B above, we assumed that there was an equal probability in the upside & downside. However, management teams would argue that the certainty of execution on projects improves with time as the management team learns and adjusts to the market and customer conditions. Accordingly, the management team may iterate the model to a wholly different binomial tree, whereby, as the project or product drives towards finalization, in our case after the “Alpha” phase and going into “Beta” phase testing, the management team may assess a 75% likelihood of an upside and only 25% likelihood of downside. Thereby, the sheer passage of time and execution certainty may result in an alignment between the utility curves of both the management team (exponential utility curve) and investor team (inverse utility curve) as seen in Table 6 below. Accordingly, both the management team AND the investors will elect Option B “revised”.
3) Conclusion & Takeaways
As with individual investors, the perception of risk plays a significant role in driving capital asset allocation decisions that may take advantage of time diversification. As a result, corporate finance professionals must pay careful attention on the impact that time diversification may have on management incentives and investor’s perception of risk.
More importantly, if managers are able to influence the probabilities with time, then it may be beneficial to outline a different dimension to time diversification in corporate finance decision, whereby managers can use milestone based targets in guiding investors to deploy capital in a phased manner and liquidating in the event there are significant deviations.