Chapter 18:Risk Analysis

Introduction to Risk AnalysisRisk is the probability that events will not occur as

expected.

Actual return may differ from the expected return.

Risk is important for several reasons:Investor’s expected return depends on risk.Risk must be considered when selecting comparable

sales.Discount rates must reflect level of risk.

Types of RiskSpace Market Risk

Risk due to changes in the market for real estate space.Can result from changes in the supply or demand for

space.

Capital Market RiskRisk that changes in the market for capital will affect

value.Caused by changes in mortgage interest rates or equity

yield rates.Affects investors even if they do not use debt financing.

Types of RiskFinancial Risk

Results from the use of debt financing (leverage).Leverage can increase expected return.Leverage always increases financial risk.

Liquidity RiskThe difficulty of converting an investment into cash at a

price close to market value within a reasonable time.Real estate has a relatively high degree of liquidity risk:

Not publicly tradedRelatively few buyers for a particular property at a

given point in time

Types of RiskInflation Risk

Risk that unexpected inflation will cause future income from operations and reversion to lose purchasing power.

Historically real estate has not had much inflation risk.Inflation tends to increase replacement costMarket rents can increase with inflationLease provisions like CPI adjustments and expense

pass-throughs help protect owner against unexpected inflation

Real estate may have more inflation risk in a weak market

Types of RiskEnvironmental Risk

Risk that environmental factors will affect ability to develop or lease space, e.g., asbestos or toxic waste

Often difficult to measure and the cost to cure the problem can exceed the value of the property.

Legislative RiskRisk do to changes in laws and regulationsExamples

Federal income tax lawsEnvironmental regulationsChanges in zoningChanges in land-use regulationsBuilding codes

Types of RiskManagement Risk

Risk resulting from poor management.Properties requiring specialized management such as

convention hotels and regional malls have greater management risk.

Sensitivity AnalysisMeasures how changes in one of the assumptions

affects the performance of the property.

Scenarios are alternative assumptions about how the property might perform.Considers interactions between assumptions.Pessimistic, most likely and optimistic scenarios are

typically considered.

Expected ReturnReturns may be for calculated for different scenarios

The expected return is found by weighing each return by its probability of occurrence

Expected Return

Scenario Overall Yield Probability

Pessimistic 5 0.3

Most likely 10 0.4

Optimistic 20 0.3

Expected Return = 0.05(0.30) + 0.10(0.40) + 0.20(0.30) = 0.1150 or 11.50%

€

E(x) = μ = x f (x)∑

Variance and Standard DeviationVariance is a measure of the uncertainty or risk

associated with an investment.

Measures the tendency of individual returns to vary from the expected return.

The standard deviation is the square root of the variance.

Variance

€

Var (x) =σ 2= (x − μ)2 f (x)∑

Variance and Standard DeviationVariance = 0.30(.05-.1150)2+0.40(0.10-0.1150)2+0.30(0.20-

0.1150)2

Variance=0.003525 or 0.3535%

Standard deviation is equal to the square root of the variance.

Standard deviation = (0.003525)1/2 = 0.05937 or 5.937%

Ranking InvestmentsThe expected return and standard deviation can be

used to compare investment alternatives.

An investment with a higher expected return is not better if it also has greater variance.

Ranking Investments

  Expected ReturnStandard Deviation

Property A 9% 4%

Property B 9% 2%

Property C 10% 4%

Ranking InvestmentsSharpe Ratio = (Portfolio return – Risk-free rate)/Portfolio

standard deviation

Property A = 9%/4% = 2.25

Property B = 9%/2% = 4.50

Property C = 10%/4% = 2.50

Expected Present ValuePresent values can be calculated for different

scenarios.

The expected present value is found by weighing each present value by its probability of occurrence.

This helps convey the degree of uncertainty in the value estimates.

Expected Present Value Example

 Pessimisti

cMost Likely

Optimistic

Increase in NOI 0 2% 4%Resale in year 5 $1,000,000 $1,200,000 $1,400,000

Probability 20% 50% 30%

A property is projected to have a NOI of $100,000 in year 1.

Expected Present Value Example1. Using a discount rate of 10%, find the PV of the property

under each scenario.

Scenario Year 1 Year 2 Year 3 Year 4 Year 5 Resale

Pessimistic $100,000 $100,000 $100,000 $100,000 $100,000$1,000,00

0

Most Likely $100,000 $102,000 $104,040 $106,121 $108,243$1,200,00

0

Optimistic $100,000 $104,000 $108,160 $112,486 $116,986$1,400,00

0

Pessimistic PV@10% = $1,000,000Most Likely PV@10% = $1,138,171Optimistic PV@10% = $1,276,880

Expected Present Value Example

2. What is the expected present value?

Expected PV = 0.20($1,000,000) + 0.50($1,138,171) + 0.30($1,276,880)

Expected PV = $1,152,150

Expected Present Value Example3. Compute the Variance and Standard Deviation.

Variance = 0.20(1,000,000-1,152,150)2 + 0.50(1,138,171-1,152,150)2 + 0.30(1,276,880-1,152,150)2

Variance = $9,394,902,591

Standard Deviation = ($9,394,902,591)1/2

Standard Deviation = $96,927

Expected Present Value Example4. What range of value estimates can you predict

within 2 standard deviations of the mean?

$1,152,150 + (2 x $96,927) = $1,346,004

$1,152,150 – (2 x $96,927) = $958,296

Partitioning the IRRA method of calculating the relative contribution of

different components of cash flow

Cash flow can be broken down as follows:

1. NOIIncome from existing leasesIncome from expected lease renewals

2. ReversionCash flow from recapture of original investment

(i.e. purchase price)Cash flow from expected price appreciation

Partitioning the IRRPartitioning uses the IRR as a discount rate

The present value of each component of the cash flow stream is calculated

The total of these present values must equal the purchase price

A project with a greater proportion of its return from reversion is usually considered more risky.

Example of Partitioning the IRR An investor considers purchasing one of the following properties.

Each can be purchased for $500,000 and would have NOI and expected sales price after 5 years as follows.

PropertyPurchase

Price NOISales Price

A $500,000 $50,000 $500,000

B $500,000 $10,000 $744,204

Calculate the IRR and partition the IRR for each property.

Example of Partitioning the IRR

Property Year 0 Years 1-5 Year 5 IRR

A -500,000 50,000 500,000 10%

B -500,000 10,000 744,204 10%

Partitioning the IRR Using a 10% Discount Rate:

Property PV of NOI %PV of Sale

Price % Total PV %

A $189,539 38 $310,461 62 $500,000 100

B $37,908 8 $462,092 92 $500,000 100

Discounting the NOI and Reversion at Different RatesNOI is often considered less risky than cash flow from

reversion

Thus, the reversion can be discounted at a higher rate than the NOI

Discounting the NOI and Reversion at Different RatesA property is leased for 5 years with a net lease at

$90,000 per year. It is expected to sell for $1,200,000 in 5 years when the lease expires. The discount rate for the leased portion of the cash flow is 9%, and the discount rate for the reversion is 12%. What is the indicated value?

PV of $90,000 for 5 years @ 9% = $350,069

PV of $1,200,000 at the end of 5 years @ 12% = $680,912

Indicated value = $350,069 + $680,912 = $1,030,981

Discounting the NOI and Reversion at Different RatesAssuming the property is purchased for $1,030,981,

what is the IRR?

CF0=-1,030,981

C01=90,000 , F01=4

C02=90,000+1,200,000=1,290,000 , F02=1

IRR=11.34%

Effect of Leverage on Financial RiskAs the loan to value ratio increases the lenders

equity yield will increase if leverage is positive.

As the loan to value ratio increases the standard deviation (risk) also increases.

Effect of Leverage on Financial RiskConsider a property with a purchase price of $100,000 with

debt financing at a rate of 10% over 30 years.

ScenarioNOI per

year Resale Probability

Pessimistic $10,000 $90,000 0.3

Most Likely $12,000 $100,000 0.6

Optimistic $14,000 $110,000 0.1

Effect of Leverage on Financial Risk

Calculate the yield at loan-to-value ratios of 0%, 30%, 60%, and 90%.

Loan/Value (%)

Pessimistic Return (%)

Most Likely Return (%)

Optimistic Return (%)

Expected Return (%)

Standard Deviation (%)

0 8.31 12 15.47 11.24 2.17

30 7.57 12.86 17.7 11.76 3.09

60 5.66 14.97 23.02 12.98 5.34

90 -12.54 28.72 54.38 18.91 21.92