04_Risk and Return

Question 1

typical per annum OCC (going in IRR) rates (late 1990s vs 2005)

• For high quality (class A, institutional quality) income
• Lower quality or more risky income property (e.g. hotels, class B commercial)
• Raw Land (speculation)

Answer 1

1. 10 - 12% vs. 7-9%
2. 12 - 15% vs. 8-10%
3. 15- 30% vs. 12 - 25%

Question 2

Discount Rate =

Answer 2

= Required Return
= Opportunity cost of capital
= Expected total return
= r
= rf + RP
= y + g

Question 3

Risk Premium

CAPM

Answer 3

• 250 - 400 bps for ‘institutional’ investment property (based on NCREIF histroical average)
• 500 to 700 bps for ‘non-institutional’ investment property (smaller, higher risk, less liquid)

Question 4

r = y + g
Approach for Opportunity Cost of Capital

Answer 4

y = cap rate (less CapEx)
g = realistic growth rate [0 - 2% in most markets]

Question 5

r = rf + RP

Explain rf and RP

Approach for Opportunity Cost of Capital

Answer 5

• for typical 10 year horizon investment
• Rf = 10 year T-bond yield
• RP = 250 - 400 bps for institutional
• RP = 500 - 700 for non institutional

Question 6

2 return components of properties

Answer 6

• income return
• appreciation return

Question 7

Total Return in context of properties
Formula

Answer 7

R(i,t) = (Di,t, + Pi,t - Pi,t-1) / Pi,t-1

= [(Di,t + Pi,t)/ Pi,t-1]-1

Question 8

Suppose the Sam Sell Select Fund buys a property at the end of 2005 for $11,250,000 on behalf of its wealthy investor clients. At the end of 2006, the fund sells the property for $12,500,000 after obtaining net cash flow of $950,000 at the end of 2006.

Calculate:
* Total return
* Income return
* Appreciation return

Answer 8

Total Return = 19.5%
Income Return = 8.4%
Appreciation Return = 19.5% - 8.4% = 11.1%

Question 9

Measures of Risk and Return

Probability distribution

Answer 9

• probability distribution of Return and Risk

Return
* 𝐸[𝑅] = 𝑃1 𝑅1 + 𝑃2𝑅2 +. . + ⋯ 𝑃N 𝑅N

Variance
VAR(𝑅) =𝑃(𝑅−𝐸𝑅)^2 + 𝑃(𝑅−𝐸𝑅)^2 +
⋯𝑃 N(𝑅N −𝐸[𝑅])^2

• where E[R] is the expected return
• Pi is the probability of each outcome
• Ri is return in each outcome
• Var (R) is variance
• 𝜎 𝑅 is standard deviation

Question 10

Measure of Risk and Return

based on historic Return

Answer 10

Return (average periodic return)
*𝐸[𝑅] =1/T (𝑅1+𝑅2+..+⋯+𝑅𝑇)

Risk

VAR(𝑅) = 1/ (T-1) [(𝑅1−𝐸[𝑅])^2 + (𝑅2−𝐸[𝑅])^2 + (Rt - E[R])^2
𝜎(𝑅) = sqrt (VAR 𝑅)

Question 11

Two components of risk

Answer 11

1. Firm (asset) specific risk
   - diversifiable risk, idiosyncratic risk, unsystematic risk
2. Market level risk
   - systematic risk, market risk, non-diversifiable risk

Question 12

Investors are compensated

Answer 12

**1. for risks
2. only for risks that they rake

Any risk which can be diversified will not be compensated**

Question 13

Return is associated with risk

Answer 13

• Expected component of returns, which is due to market risks
• unexpected component of retursn due to firm specific risk

Question 14

CAPM

Answer 14

Realised Return = Expected Return + Unexpected Return

𝑅𝑖,𝑡=𝐸[𝑅𝑖,𝑡] + 𝜀𝑖,𝑡

The Expected return satisfies:

𝐸[𝑅i,t]= 𝑟 + 𝛽i (𝐸[𝑅m,t] − 𝑟f )

Question 15

Definition of Risk Premium

Answer 15

• extra return that we require relative to a less risky opporutnity
• reward investors reqiure for taking on the risk of investing in a riskier asset

Question 16

Beta

Answer 16

• systematic risk of the underlying asset relative to an average one
• shows the speed of reaction to changes in market returns
• beta = 1.5 means that asset return will be equal to 1.5*x of market return

Question 17

Risk free rate

Answer 17

pure time value of money

Question 18

Market Premium

Answer 18

𝐸[𝑅m,t] − 𝑟f