Intro

Investment decisions in the real estate sector are tackled with uncertainty. There is nothing new about that. Topics like the generally mid- to longterm investment focus, uncertainties in rent price developments, insecurities with respect to yield expectations, funding costs movements driven by factors not controlled by the investor alone, to name a view, seriously increase the general risk of an investment in this alternative segment.

Nevertheless at time of decision making a respective investor has to make certain assumptions about all the parameters influencing the investment decision and see if it is worthwhile to step in. Those assumptions are (hopefully) based on the studying of the asset class and the local market in question as well as on monitoring economic indicators possibly influencing the situation. Scenario analysis should back up the decision making process.

But, what is the risk of making those assumption? How wiggly is the framework when making those assumptions? What is the expectation of ending up in one of those scenarios outlined in the scenario analysis. We'll have a look at those questions.

Classic Core Office Investment/ an example

In order to put some light on those questions, let's take an example. A real estate investor is interested in purchasing an office building with the following rough key data:

```
asset: Office
renting area: 30,000 sqm
parking lots: 250
rent income office: 15.65 EUR per sqm and month
rent income parking: 150 EUR per lot and month
investment yield: 7.25 % p.a.
debt leverage: 70 %
rent outlook: stable
funding costs outlook: stable
expected exit yield: 6.00 % p.a.
```

As a reminder, this is an example and the figures are totally made up. The project should produce the following Cash Flow during the holding period:

```
FFO: 1.5 MEUR p.a.
Exit Cash Flow: 50.3 MEUR (selling price after deducting costs
and outstanding debt)
```

Given those circumstances and based on an equity investment in the amount of MEUR 22.5 the project is capable of offering an equity yield of 17.1 % p.a. As the expected equity yield is higher than the investor's internal minimum equity yield of 15 % p.a., the decision is a 'Go' for this project.

Scenario analysis shows that one of the main drivers for the equity yield is the exit yield at the end of the holding period. Here an overview:

```
Exit Yield Equity Yield
(in % p.a.) (in % p.a.)
----------------------I-----------------I-------------------
Best Case Scenario I 5.25 I 19.7
Banking Scenario I 6.00 I 17.1
Worst Case Scenario I 6.75 I 14.6
```

The exit yield should be the point where the investor "lands" at the end of the holding period. In this case, this is 5 years from now opening a big gap of uncertainty simply given by the underlying time line. So how to get a grip on this uncertainty? How can the possible realisation of a scenario be quantified and how to frame the risk connected with, in this case, different exit yield developments?

The basic question in this setup is: "What is the risk of diving below the internally required minimum equity yield of 15 % p.a.?"

Exit Yield - the range approach

In a first approach, the uncertainty within the exit yield expectation in five years from now is taken into account by means of allowing the exit yield to swing within a certain range. Let's assume we expect the exit yield swing between 5.25 % p.a. and 6.75 % p.a. according to the investor's scenario analysis. After running a Monte Carlo simulation the distribution of possible exit yields within this range is as follows:

resulting in the following range of possible equity yield results:

What do we see here. The investor faces a range of possible equity yield outcomes between 14 % p.a. and bit over 20 % p.a. The dashed black line represents the expected equity yield of 17.1 % p.a. calculated as banking scenario in the investment proposal. The straight black line represents the required minimum equity yield of 15 % p.a as determined by the investors. What is more important, according to this approach there is a rather low probability of 16 % that the project will not match the internally determined minimum equity yield.

Exit Yield - taking historical data into account

In the monitored time period, the (hypothetical) historical yield for office buildings in the relevant local market came from 8.9 % p.a. and already reached a level of 5.8 % p.a. before harshly reversing. Afterwards yield development again shows a decreasing trend with a current yield level of appr. 7.3 % p.a. Also see chart below:

Based on this data and running a Monte Carlo simulation the investor can expect a distribution of exit yields as shown below (i.e. the brown area; blue dashed line represents the exit yield of 6 % p.a. according to the initial investment calculation):

It seems that the investment team was quite optimistic about the development of the exit yield as those indicated 6 % p.a. are on the edge of possible values. And not surprisingly, the calculated equity yield of 17.1 % p.a. (banking scenario) also represents an event on the edge of possible values (see chart below: the green area is the space of possible equity yield results; the straight line equals the required minimum equity yield of 15 % p.a.; the dashed line represents the equity yield of 17.1 % p.a. according to investment calculation):

Why is this not surprising? Given the (hypothetical) historic data the average exit yield amounted to around 7.4 % p.a. with a volatility of close to 1 % p.a. The presumed exit yield according to investment calculation of 6 % p.a. is therefore on the edge of possible outcomes. So in this scenario, the chances of the project for not matching the required minimum equity yield are an amazing 82 %. Hence, there is high risk of buying into a project which will not come up to earnings requirements implemented by the equity investors.

Exit Yield - taking own expectations into account

So far, we got two extreme results. On the basis of just guessing a range of exit yield values (we called it the 'range approach' which is, after all, just an 'educated guess'), the chances of the project not achieving the minimum equity requirement were quite low, i.e. around 16 %. On the other hand, relying on pure market data showed a high risk of failing of appr. 82 %. Of course, the reliance on hard facts is to be preferred to outright guessing.

Although, what is missing in the pure market data approach is the implementation of a trend respectively the market opinion of an investor. After all the decision of investing in a real estate market is based on detailed market research and an elaborated market opinion which also includes an exit yield expectation. And this should find its weight in the risk verification. Yes, we allow for bias in the risk assessment. And handling the parameters which lead to this market opinion/ bias is another very interesting topic.

In our example there is an optimistic notion about the further yield development in the market. In order to reflect this belief, the underlying risk model allows for lower yield rates to happen more frequently. This is shown in the chart below.

In short, the red line in the left graph shows the yield distribution based on pure market facts as we had it in the previous chapter. The grey bars show the yield distribution incorporating the positive market opinion of the investor. What can be clearly seen is the yield distribution shifting to the left towards lower yield rates (a left skewed distribution). In other words the model allows for a fatter tail (i.e. more occurrences of events on the edge) in favour of the investment (an 'opportunity tail' so to speak). The dashed blue line represents the exit yield rate of 6 % p.a according to initial investment calculation. The right graph once more shows quite explicitly the movement towards lower exit yield rates (i.e. the shift of the black points from the straight blue line in the bottom left area).

To summarise. We implemented the following exit yield possibilities (brown area; blue dashed line again is the initially calculated exit yield of 6 % p.a.) based on a more favourable market expectation:

which leads us to the following equity yield expectation (red space; dashed black line equals the equity yield of 17.1 % p.a. according to initial investment calculation; straight black line is the required minimum equity yield):

As a result and based on the framework described above, the risk of not achieving the internally required minimum equity yield of 15 % p.a. is close to 60%. So, incorporating a positive market belief shows, of course, a reduction in the risk assessment. Though, what is more important is the fact that despite incorporating a favourable market opinion the risk of not achieving the required minimum equity yield is still high und puts a different light on the promised 17.1 % p.a. First of all, the investment is definitely not a sure bet with respect to internal earnings requirements and the investment team still could be overoptimistic regarding exit yield developments.

Conclusion

Given the circumstances in the alternative investment segment real estate, uncertainty is a persistent constant in the decision making process. The incorporation of suitable risk models for quantifying the uncertainty and helping to make a proper risk assessment is therefore an absolute necessity for investors.

This article shows the risk accompanied with an office investment failing to match an earnings benchmark required by the investors. The risk model allows for market opinion to be incorporated. But by relying on market data at the same time, an overoptimistic view on the risk situation is prevented. Same risk models can be used to monitor single projects respectively whole portfolios already invested in. Frequent risk assessments on an automated basis allow for early time windows in adjusting an investor's position. After all an 'opportunistic tail' could at one point of time turn into a fat tail risk.

This here is just one example. The building of suitable risk models depend on the questions in place, the proper use of in-house and external data and -last but not least- on using the benefits of digitalisation in the decision making process.

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