Microsoft Word – Class 6&7 33450 23 Supplement_v1.1.doc
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Real Estate Investments I
Instructor: . Pagliari, Jr.
Class Notes – Weeks #6 & 7:
Mortgage Debt/Use of Financial Leverage – Supplement
Table of Contents
I. How to Think of Unlevered (ka) and Levered Returns (ke) …………………………………… 1
II. The Riskiness of Levered Equity (e) ………………………………………………………………… 4
III. A Risk/Return Comparison ………………………………………………………………………………. 5
IV. Does the Market Understand Leverage? A Dissenting Opinion ……………………………. 8
V. Does the Amount of Leverage Effect Asset Performance? ………………………………….. 10
In order to think strategically, you must understand the mechanics!
I. How to Think of Unlevered (ka) and Levered Returns (ke)
A. Suppose that someone offers you two investments:
1. Project A offers an expected return of 14.2% (see Homework #4).
2. Project B offers an expected return of 15.0%.
3. Which would you pick?
Assume both properties are in the same area and are the same property type.
B. Suppose you are prudent enough to ask about the return-generating process for each of the
projects. You are told the following:
1. Project A’s and B’s components of E(ka) are:
IRR Attribution: Project A Project B
Initial Yield 7.25% 6.00%
Inflation Rate 3.00% 3.00%
Base Yield 10.25% 9.00%
Market Disequilibrium -1.50% -1.00%
Total Asset Return (k a ) 8.75% 8.00%
2. Now how do you feel about your choice (Project A v. B)?
Q: What do the components of return suggest about the likelihood of achieving the
forecasted or expected return?
A: Differences may be attributable to ():
differences in submarkets,
differences in property quality,
differences in tenant quality,
differences in optimism (e.g., two different underwriters), etc.
A reason cannot be given with certainty, based on the information provided. However,
the answer in an efficient market would be that the differences in expected returns
[E(ka|A) v. E(ka|B)] is a function of the differences in their risk [a|A v. a|B].
This is why shrewd investors ask questions; they just don’t take the numbers at
face value.
Thinking about how to approach this problem is like pulling back the layers of an onion.
information
provided so far,
you cannot
reasonably make
a decision.
information
provided so far,
you still cannot
reasonably make a
C. Ignoring potential shifts () in the capitalization rates, what does that tell you about the effect
of leverage on each?
1. It must mean the following:
IRR Attribution: Project A Project B
Initial Yield 7.25% 6.00%
Inflation Rate 3.00% 3.00%
Base Yield 10.25% 9.00%
Market Disequilibrium -1.50% -1.00%
Total Asset Return (k a ) 8.75% 8.00%
Effect of Leverage 5.43% 7.00%
Total Equity Return (k e ) 14.18% 15.00%
2. What is implied about the leverage ratio of Project B?
Assume each project has the same debt cost (kd = 6.79% – see Homework #4).
This implies: e a
Here’s the algebra for Project B’s LTV ratio:
1500 1 0800 0679
1500 1500 0800 0679
1500 0800 1500 0679
0700 1500 0679
Q: What was the LTV
ratio for Project A?
A: 73.5%. (HW #4)
(ke – ke )
3. Now, how do you feel about your choice (Project A v. B)?
Q: Does it seem accurate to assume both projects have same kd?
A: While it was earlier questioned as to whether a|A > a|B [given that E(ka|A) >
E(ka|B)], there is not enough information provided to know.
However, if they have identical (or even similar) asset-level volatilities, it does not:
0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85%
Loan-to-Value Ratio
Illustration of the Cost of Indebtedness as f(LTV)
for a Given Maturity Date
kd | A ≈ 6.79% (from Homework #3)
kd | B ≈ 8% (“eyeballed”)
LTVA = 73.5%
LTVB = 85.3%
II. The Riskiness of Levered Equity (e)
A. Let’s assume each of the projects have the same asset-level volatility (a) = 6.0%.1
B. Q : Do you think that’s a fair assumption (i.e., the projects have identical a)?2
A: Not likely.
C. Notwithstanding the arguments above and for the sake of simplicity, let’s assume that the asset-
level volatilities are identical. Then, let’s calculate the implied volatility of the levered equity
returns (e).
D. Recall the riskiness of levered equity (using fixed-rate financing):
E. The expected volatilities3 are then:
Assumed Equity Volatility (e) =
Project A Project B
22.64% 40.81%
F. Now, how do you feel about your choice (Project A v. B)?
1 As earlier mentioned, this is quite low by NCREIF standards. [You should be able to work through the math if
a was higher (e.g., a = 10%), which would lead to levered equity becoming much riskier!]
2 The probabilities of each property achieving its expected returns are identical if the volatility inherent in future
cash-flow growth, capitalization-rate shifts, etc. are identical.
3 If you are uncomfortable (I am) with the (unsupported) assertion that the two assets have the same risk, what
would the volatility of Project B (a|B) have to be in order for the volatility of levered equity to be equal to one
another (a|A = a|B)?
1 .735 1 .853
Note: Changing your estimate of Project B’s volatility of would also effect your estimate of the project’s debt cost.
← way too low!
III. A Risk/Return Comparison
A. Looks like not much of an increase in the expected return on levered equity (difference of 0.8
percentage points) for a substantive increase in risk (difference of 18.0 percentage points):
0% 5% 10% 15% 20% 25% 30% 35% 40% 45%
Volatility of Expected Return [e]
Projects A & B in Risk/Return Space
To reiterate: Shrewd investors ask questions!!
ke | B ~N( 15.0%,40.8%2)
ke | A ~N( 14.2%,22.6%2)
B. What would the 4 (recall: f
) suggest about these two projects?
0% 5% 10% 15% 20% 25% 30% 35% 40% 45%
Volatility of Expected Return [e]
Projects A & B in Risk/Return Space
Risk-Adjusted
ShortfallB
C. How do you feel about the “downside” risk?
Q: What is the probability for of each of the projects earning less than 0% (i.e., “losing
money”) assuming the returns are normally distributed?
A: 0 | ~ ,e e e eProb k k N k =
Project A Project B
26.56% 35.66%
4 More fundamentally, what would the volatility of Project B (a|B) have to be in order for the two investments to
offer the same Sharpe ratio (SRA = SR B)? To sketch the exercise:
Reminder: Changing your estimate of the volatility of Project B (a|B) would also likely effect your estimate of the
project’s cost of indebtedness (kd|B) and, in turn, the project’s leverage ratio (LTVB).
D. A plot of the distributions looks like:
-100% -50% 0% 50% 100% 150%
Range of Outcomes
Illustration of Return Distributions
E. Among practitioners:
1. Risk is difficult to express (see week #9).
2. Risk tolerance (or aversion) is even more difficult to express (see week #9).5
5 Among the relevant concepts is the idea of utility (or prospect) theory. The basic premise is quite simple:
investors prefer bigger gains to smaller gains but at a declining rate; as such, most investors exhibit some form of
risk aversion.
~N(14.2%, 22.6%2 )
~N(15%, 40.8%2 )
IV. Does the Market Understand Leverage? A Dissenting Opinion
A. In an earlier class, I made the (bold) statement that the real estate market, by and large, does not
understand the mechanics of leverage with regard to risk and return. Certainly, that is a
statement that should be challenged – particularly at a place like Chicago Booth which, as a
general rule, strongly believes in the efficiency of markets.
B. Moreover, I’d argue this deficiency is not confined to the real estate market. It is also apparent
in the buyout/private-equity arena.
C. Consider the following table and accompanying text6 (some of which is highlighted):
6 Source: . Swensen, Pioneering Portfolio Management, An Unconventional Approach to
Institutional Investment, Free Press, 2000, p. 232.
A debt-to-
equity ratio of
5.2:1 translates
to a leverage
ratio of 84%.
Similarly, a
debt-to-equity
ratio of 0.8:1
translates to a
leverage ratio of
Buyout Investing:
Gross Return 48%
Fees & Costs -3%
Pre-Promote
LPs’ Share 80%
LPs’ Net Return 36%
D. Consider the results:
1. Buyout investors “lost” approximately 38 percentage points (i.e., 3,800 bps) to a levered
S&P 500 strategy – before investment management fees.
2. Buyout investors “lost” approximately 50 percentage points (i.e., 5,000 bps) to a levered
S&P 500 strategy – after investment management fees.
E. How do you feel about the market’s understanding of leverage?
F. Since the original publication of Swenson’s book, consider at least two troubling items:
1. The second edition of his book did not update this table. (The silence may be telling).
2. The more-recent academic research in this area has disputed these conclusions about private
equity’s underperformance. For example, see:
, Bingxu Chen, . Goetzmann and ,
“Estimating Private Equity Returns from Limited Partner Cash Flows,” 2013, Columbia
University working paper.
. Harris, and . Kaplan, “Private Equity Performance:
What Do We Know?,” Journal of Finance, 2014, pp. 1851-1882.
. Harris, and . Kaplan, “How Do Private Equity
Investments Perform Compared to Public Equity?,” Journal of Investment
Management, 2016, pp. 1-24.
. Robinson and . Sensoy, “Do Private Equity Fund Managers Earn Their
Fees? Compensation, Ownership and Cash Flow Performance,” Review of Financial
Studies, 2013, pp. 2760-2797.
G. Nevertheless, while the marketplace’s understanding of leverage may have improved (indeed,
much improved) – at least from the perspective of (non-real estate) private equity – I’d still
suggest that marketplace’s understanding is far from universal – particularly with regard to real
estate private equity (see: “Core v. Non-Core Real Estate…” in RE II).
V. Does the Amount of Leverage Effect Asset Performance?
A. The classical M&M arguments assume that the performance of asset-level returns is invariant to
the level of leverage.
B. Q : Yet, could it be the case that high levels of leverage adversely affect asset performance?
A: Yes, these adverse effects are often referred to as the “costs of financial distress.”
C. Consider this analysis of the REIT market as prepared by Advisors: “Heard on the
Beach,” April 1, 2008:
D. Q: What do you think is driving the disparity in performance (i.e., the downward-sloping
regression line) between high- and low-levered firms?
1. A: Kirby | :
(a) Coincidence – bad firms happened to have higher leverage. But, given the large sample
of firms, this is unlikely.
(b) Excess leverage during the downturn (early 2000s) led to bad firms unable to participate
in opportunistic acquisitions. Worse yet, their (occasional) “financial distress” caused
them to issue additional equity – at the wrong time – which was dilutive to existing
shareholders (see week #8 note).
Boston Properties
Avalon Bay
Simon Property Group
General Growth
Highwood Properties
Colonial Properties
Post Properties
This is a really good decade to be a CRE investor!
Best-performing REIT
(high-quality office buildings in
high-barrier markets)
Worst-performing REIT
(sun-belt apartments – merged
with MAA in 2013)
2. A: Pagliari | RE I: Agree with Kirby/ , but add:
(a) Unsophisticated investors initially overpay for the shares of more highly levered firms
(ultimately, they are disappointed and shares sell off at lower prices).
(b) Because lenders requiring increasingly higher coupon payments with increasingly higher
leverage ratios (as compensation for increasing default risk), the levered risk/return
continuum is flatter than Kirby| assert. (In other words, the lenders
appropriate some increment of the asset return as the leverage ratio increases.) Recall
from earlier:
0% 2% 4% 6% 8% 10% 12% 14% 16% 18%
Volatility of Expected Return ( e)
Exhibit 11: Illustration of the Expected Return and Volatility
of Levered Equity Returns (Riskless v. Risky Debt)
0% Leverage
75% Leverage
50% Leverage
25% Leverage
Risky Debt
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