Now that we are almost halfway through the book, it is a good time to take a break from the math and graphs and think about some of the contextual issues in using simulation to explore our alternatives for flexible management of real estate.

10.1 Sensitivity Analysis

Simulations of flexibility provide us with masses of data. We can analyze this information to gain additional insights beyond investment performance targets such as PVs and IRRs.

For example, simulation analysis allows us to see the effect of resale timing flexibility on the various metrics of investment performance. Since the simulation keeps track of when the IF statement indicates that it is desirable to sell, we can see how this flexibility affects the average holding period for the property. How frequently does the simulation say we will hold the property for more than 10 years? Or for less than 5 years? In our example with a 20%‐trigger stop‐gain resale rule, detailed analysis of the results indicates that the average holding period for the investment is just barely less than the 10 years assumed in the pro forma. The median holding period is between 7 and 8 years. We hold the investment all 24 years in the potential horizon in just over 10% of the scenarios. These statistics mimic typical property investment holding behavior in the United States, which gives us some confirmation that the 20% stop‐gain rule might in fact not be too different from what many investors actually do. (Of course, this presumes, as we believe, that our input price dynamics assumptions are based on solid knowledge and empirical evidence about the nature of commercial property price dynamics in the United States.)

By rerunning the simulation, we can furthermore carry out a sensitivity analysis. We can explore how different assumptions or specifications of the flexibility would change the results. For instance, we could add more conditions to the resale rule, such as requiring a minimum hold or setting a maximum hold of less than 24 years, or requiring additional simulated conditions to exist or not exist for the resale.

In our case, we explicitly tested different trigger levels. The result was that the 20% trigger level we examined seems to be quite good, although its performance nearly equals any trigger level between 15% and 25% in terms of the PV and IRR target curves. The insight we can derive from this sensitivity analysis is that flexibility in timing the resale for this example is beneficial, adding value and improving investment return performance, and that it’s not worth much argument about the exact trigger level roughly around +20%.

We can also slightly modify the simulation to explore variations of the timing rule. Thus, we also explored a stop‐loss decision rule. Such a rule triggers us to sell as the price goes down. However, that rule does not work well for our real estate case. The stop‐loss rule locks in the loss implied by its trigger level, even though mean‐reversion, or even just random volatility, causes the property’s prospects to tend to improve after a down period.

10.2 When to Use the Stop‐Gain Rule

The stop‐gain rule is a logical resale decision rule for real estate because the price dynamics for real estate display cycles and mean‐reversion. These drive the value of stop‐gain rules. Price dynamics without these factors—dynamics that more typify stock markets—do not allow the stop‐gain rule to add value to the asset (holding the discount rate constant), although the stop‐gain rule can still improve the IRR performance of the investment (at a given price).

Further analysis of the simulation model allows us to note that the value of the stop‐gain rule depends on when (at what point of the cycle) we apply the rule. In our simulation model, we allow the cycle to vary randomly and uniformly between 10 and 20 years in length, and with a starting phase that also varies uniformly across all phases (peak, trough, and every phase in between). In other words, our analysis is agnostic in terms of where we presently are in the market cycle as of Time 0, the time of the investment decision (and of the PV analysis).

But in the real world, market participants often have a good impression about where they are in the relevant property market cycle, or at least, they should be able to have such an impression. This is especially possible if there is good data about current pricing in the market and some history about market pricing trends, such as histories of rents or vacancy rates, and property transaction price indices or historical data on yields and capital flows in the market.

The simulation model allows one to see the points in the cycle where the stop‐gain rule adds the most value. It depends on the length of the cycle period, but, in general, the rule is pretty robust, no matter where you are in the market cycle. Even at those points in the cycle where the flexible rule performs worst, the 20% stop‐gain resale provides a mean ex‐post PV not much below that of the inflexible 10‐year resale.

10.3 Implications of Flexibility for Property Valuation

Let us return to a rather intriguing point that we glided over in the previous chapter: the finding that the value of the property with the flexibility seems to be greater than the property’s market value. Specifically, the simulation indicated that the mean ex‐post PV of the property investment with the stop‐gain rule was around $1250, based on the market OCC of 7%. This valuation is about 25% more than the $1000 estimate of the market value from the traditional DCF valuation model based on the 7% OCC and the single‐stream cash flow projection that is the unbiased expectation of the property cash flows. (And we noted that $1000 is also the mean ex‐post PV at the 7% OCC in the simulation with forced resale at Year 10.)

Is the property really only worth $1000? Wouldn’t $1250 be a better estimate of its value, ex‐ante? This $1250 is the mean of the ex‐post present value results (at the 7% discount rate) that are possible with a plausible representation of resale decision timing flexibility (assuming our simulation reflects realistic property price uncertainty and dynamics). If 7% is indeed an accurate estimate of the OCC (as discussed in Chapter 2), the property seems to be worth more than its $1000 market value, estimated using the traditional DCF valuation model. What are we to make of this?

A key point to recognize is that, while the flexibility simulation analysis is relevant for potential investors, it is not a model of the equilibrium price, or market value, of the property. The value resulting from the flexibility analysis relates to the private value of the property, as we defined this term in Chapter 2. The market value could well be the $1000 we originally estimated. If so, then that means, from the private or investment value perspective of an investor who will follow the stop‐gain decision rule (with the 20% trigger), a purchase of the property at the market value price would present a windfall value (positive NPV) of $250. Briefly put, a smart investor could use flexibility to outperform the market!

However, in this regard, it is important to consider that the investor’s ability to profit from the resale flexibility according to our stop‐gain rule is not certain. It depends on several factors. Will the investor be able to:

• Implement and have the discipline to adhere to the 20% stop‐gain decision rule? This will require sufficient information to be able to judge (at least approximately) when the current market for the property breaches the effective equivalent of the “20% trigger.”
• Carry out such a resale decision discipline, which may involve selling quite early, or holding on quite long? In fact, it might be inconvenient to sell just whenever the market happens to breach the 20% trigger. What will the investor do with the proceeds at that time? Might the investor need to cash out on the value of the property sooner? There is some loss of flexibility when you commit to a strict rule, no matter what that rule is. The relevant decision environment is not just this one property in isolation, but other business and investment considerations that the investor may have. (On the other hand, the automatic, inflexible resale at Year 10 implied by the traditional pro forma might be just as, or even more, unrealistic or difficult to implement.)

These considerations bear upon why the market equilibrium price could well differ from the $1250 value.

We should also consider the other side of the deal: the party who buys the property from the investor when the stop‐gain rule is triggered for the resale. What makes the rule work is mean‐reversion in the property market. This suggests sales only when prices are relatively high, likely to trend downward, or at least likely not to trend abnormally upward going forward from the sale date for at least a few years. In fact, in real estate investment markets, we do observe a positive correlation between transaction volumes and sale prices. But if everyone adopted the stop‐gain rule, we would never see any sales when prices are down (which is counter‐factual), and sellers, triggering their stop‐gain rules, should have difficulty finding buyers when prices are high (which is counter‐factual). Widespread adoption of the stop‐gain rule would seem to be incompatible with the property market functioning as smoothly as it usually does, unless there is substantial disagreement among investors about where they are in the cycle. This suggests that, in the real world, many investors have trouble with at least one of the bullet points presented in the preceding list.

Finally, it is important to recognize that the mean of a target curve is only one aspect of the performance of the investment. The investor may also care about other features of a target curve, such as the downside tail or the upside tail. And the investor may care about other metrics besides the present value, such as the IRR. In the present example, as you can see from Figures 9.2 and 9.3 and our discussion of the scatterplot in Figure 8.6, the stop‐gain decision rule produces good results from those other perspectives as well. But this will not always be the case.

With these considerations in mind, the suggestion is that a sophisticated investor might use flexibility to identify and exploit hidden value that most other investors do not appreciate—and, therefore, which the market does not recognize or price. The traditional DCF pro forma could correctly identify $1000 as the current market value of our subject property. But flexibility analysis using simulation reveals the potential for significant profits. It suggests that we could buy the property for $1000, and yet obtain an asset worth $1250 to us (in a private valuation sense), provided we have the flexibility, discipline, and information necessary to carry through with a particular investment resale strategy.

Flexibility analysis thus has important practical implications for real estate business strategy and tactics. That’s the reason for this book. That’s why we’re presenting this modeling and analysis. Perhaps, in time, all real estate investors will understand and exploit flexibility analysis, and the profit gap between private and market values may disappear. Until then, those who understand and can analyze the value of flexibility should have a significant advantage.

10.4 Conclusion

The discussion in this chapter places flexibility analysis using simulation in a larger context. From a tactical perspective, it indicates how we can use simulation to explore assumptions and details of plans to manage our risks in our uncertain world. Strategically, it emphasizes that sophisticated investors can use flexibility to identify and exploit hidden value that the market may not recognize or price.