Other Valuation Tools and Portfolio Diversification

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Other Valuation Tools and Portfolio
Diversification

• Session Eight

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Valuation of Income Producing Properties

• Objective Estimate market value as oppose to
  investment value
• Definition of market value
• most probable price which a property should bring
  in a competitive and open market under conditions
  requisite to fair sale, the buyer and seller
  acting prudently and knowledgeably, and assuming
  the price is not affected by under stimulus
• Market value is not necessarily equal to
  investment value

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Relation between Market Value and Investment Value

• If investors discount rate is higher than the
  markets, investment value will be lower than
  market value, holding constant cash flow
• If investors time preference is lower than the
  markets, investment value will be higher than
  market value, ceteris paribus
• If the rate of discount for the investor is equal
  to that of the market, market value will equal
  investment value
• What is the implication of these relationships on
  real estate investment strategy?

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Valuation Methodologies

• Income capitalization approach
• Gross Income Multiplier
• Net Income Multiplier
• Direct sales comparison approach
• Cost Approach

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Income Capitalization Approach

• The income capitalization approach is the most
  meaningful approach in valuing income-producing
  properties
• Premise market value of real estate is the
  capitalized value of anticipated or expected
  income stream
• The basic model is as follows
• V NOI/R
• WHERE
• V market value
• NOI net operating income
• R capitalization rate or cap rate for short

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Developing Net Operating Income

• Potential Gross Income
• less Vacancy and Bad Debt
• Effective Gross Income
• Operating expenses
• wages
• utilities
• management
• real estate tax
• insurance
• maintenance/repairs
• Replacement Reserve
• Net Operating Income (stabilized Net Operating
  Income)

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Income Capitalization Approach

• (1) Direct Capitalization
• To apply this technique one needs a sample of
  comparables recently sold, from which the
  capitalization rate is extracted as follows
• A B C D
• Sale price 3,250,000 3,500,000
  3,350,000 3,200,000
• NOI 346,125 390,250
  325,000 310,250
• Cap rate 10.65 9.94
  10.31 10.31
• Suggested cap rate 10.42
• Estimated NOI of subject property 338,000
• Market value of subject property
  338,000/.1042 3,243,762

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The perpetuity Valuation Model
Start with the notion that value of income
producing property is equal to the present
value of the future cash flows generated by the
property
Assume the operating income or NOI grows at
constant rage g then the valuation model is
The above equation compresses to
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Present value method with income in perpetuity

• If income and property value are changing at the
  same rate
• V NOI1/(R - g)
• where g growth of income which is equal to rate
  of appreciation of property value
• Assume investors discount rate 13, and g
  2.5 NOI1 338,000
• Propertys economic life 80 years (equivalent
  to holding the property to perpetuity)
• V 338,000/(.13 - .025) 3,219,047
• Note If we assume a specific holding period
  instead of perpetuity, which is more realistic,
  the estimated market value should be essentially
  the same.

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Example Financial Feasibility Analysis Assume a
20-unit apartment complex is being considered for
a commercial mortgage loan. The estimated market
value of the property is 280,000. The borrower
would like to obtain a 75 loan on the property.
The interest rate on the commercial mortgage loan
will be 9, amortized over 25 years, although the
term of loan is 15 years. The operating statement
of the property is as follows Operating
Statement Potential Gross Income
60,000 Less
vacancy and bad debt
4,200 Effective Gross Income

55,800 Less
Operating Expenses Management

2,800 Utilities
500
Maintenance
2,400 Repairs

1,900 Insurance
900
Taxes
2,800 Other
Expenses
2,000 Reserve

1,100 Total Operating Expenses

14,400 Net Operating Income
(NOI)
41,400
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Financial Ratio Analysis
Debt Coverage Ratio (DCR) 41,400/21,147.74
1.95 Operating Expenses Ratio (OER)
14,400/60,000 0.24 OR 24 Break Even Ratio
(BER) (14,400 21,147.74)/60,000 0.83 OR
83 Return on Assets (ROA) 41,400/280,000
0.1478 OR 14.78 Net Income Multiplier (NIM)
Market Value/NOI 280,000/41,400
6.76x Gross Income Multiplier (GIM) Market
Value/PGI 280,000/60,000 4.7x Loan Amount
(.75)(280,000) 210,000 Debt Service PV
210,000 I 9/12 N 25X12 COMP PMT
1762.31 Annual Debt Service (1762.31)(12)
21,147.74
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Direct Sales Comparison Approach

• Sales comparison approach
• Basis or Rational for the model
• Comparable property
• Subject property
• Rule for adjusting prices
• Regression (Hedonic) approach

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Cost Approach

• Cost Approach
• Rational for the model
• Types of depreciation
• Curable and incurable depreciation

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Real Estate Investment Performance and Portfolio
Diversification

• APPENDIX

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The Risk-Return Trade Off

• Like other investors, real estate investors face
  several risks including business risk, default
  risk, and liquidity risk
• Evidence shows that most investors are risk
  averse
• The amount investors will give up to avoid taking
  on a risky investment is called risk premium
• Alternatively, the higher the riskiness of the
  investment the higher should be the expected
  return to induce investors to hold that
  investments (see exhibit 1)
• This relationship is also stated as follows
• Where r the required rate of return rf the
  risk-free rate of return and p risk premium

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Exhibit 1 The Basic Risk-Return Relationship
C
Required Rate of Return
Risk premium
B
rf
A
Risk-free rate of return
Risk
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Elements of Portfolio Theory

• The traditional portfolio theory
• The traditional portfolio theory started from
  Markowitz (1952) and expounded in every finance
  textbook
• According to the mean-variance portfolio theory,
• Investors should seek to minimize the variance
  (volatility) of portfolio for a given an expected
  return
• Investors should seek maximize expected return
  for given risk

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Elements of Portfolio Theory

• Exhibit 2 summarizes the analysis behind this
  objective
• The indifference curves simply say that investors
  want portfolios with greater mean return and
  lower return variance or volatility
• This will be portfolios that are higher up and to
  the left
• This means investors are willing to accept more
  risk only if they can get higher average returns
• The mean-variance frontier (efficient frontier)
  gives the minimum possible variance of a
  portfolio return for each level of mean portfolio
  return

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Average Return E(r)
Mean-variance frontier
Investors want
C
Risky asset frontier
Optimal portfolios
Market portfolio
B
Original assets
A
rf
Volatility s(r)
Exhibit 2 Mean-variance frontier, optimal
portfolio and two-fund theorem
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Portfolio Performance Measures

• Portfolio Total Return
• The formula for computing the arithmetic mean
  return is
• Where A value of asset A B value of asset B
  AB combined value of the portfolio a
  percent invested in portfolio A and therefore
  (1-a) is percent invested in portfolio B
• Variance of the Portfolio
• The variance of this two asset portfolio is
• Where is the variance of the portfolio
  is the variance of the return on asset A
  is the variance of the return on asset B and
  COV(A, B) is covariance of the returns on A and B

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Performance Measures

• To implement the portfolio variance equation we
  need to know the variance of the individual
  assets. For example the variance of asset A
• Where is the ex post mean return for a series
  of T periodic returns (r1, r2, rT)
• The standard deviation, which is simply the
  square root of the variance, (or volatility) has
  advantage over the variance as measure of risk
• This is because it is measured in units of
  returns
• Note also that standard deviation of portfolio
  returns or volatility is not equal to the
  weighted average of the individual standard
  deviations of the two assets
• We need to consider also the interaction between
  the two returns

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Portfolio Performance Measures

• Covariance of asset returns
• This is a measure of the extent to which the
  asset returns in the portfolio move together
  across time
• If the covariance is positive the returns move in
  same direction, if its negative they move in
  opposite direction, and if its zero the two
  assets are unrelated
• The economic significance of covariance is that
  the covariance between an asset and portfolio is
  the component of the assets variance that is not
  diversified away when the asset is added to the
  portfolio
• So covariance is basic to measuring systematic
  risk
• Also if an asset return moves in tandem with the
  portfolio return, then the inclusion of the asset
  in the portfolio will not reduce total risk of
  the portfolio by much

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Portfolio Performance Measures

• Correlation of Returns
• Because the covariance statistic is an absolute
  measure it is difficult to interpret as a measure
  of co-movement between asset returns
• The correlation coefficient is relative measure
  of the extent to which asset returns move in the
  same or opposite direction. In our two asset
  portfolio the correlation coefficient is stated
  as follows
• The value of correlation coefficient ranges from
  1 to 1
• For diversification to reduce portfolio risk the
  correlation coefficient has to be less than one.
• An asset with correlation coefficient of close to
  zero will yield the most benefit to the portfolio

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Performance Measures

• The Sharpe Ratio
• In Exhibit 2 we used geometry to determine that
  point B is the combination of the riskless asset
  and the risky asset that is the unique optimal
  allocation
• Another way to make the same determination is to
  calculate the Sharp Ratio
• Thus the Sharpe Ratio gives the excess return for
  every percentage increase in standard deviation (
  risk)
• In the presence of riskless asset the optimal
  combination of risky asset is the one with
  highest Sharp Ratio
• The Sharp Ratio is widely used by practitioners
  because it is very intuitive

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Traditional Portfolio Advice

• Portfolio Advice The Two-fund theorem
• Note that every portfolio on the efficient
  frontier can be formed as a combination of the
  risk free asset and the market portfolio
• From this analysis, the simple advice is that
  every investors need only hold different
  proportions of the two funds -- the two-fund
  theorem
• Of course the complete portfolio formed will
  depend on investors risk aversion
• But both risk-averse investors and risk-tolerant
  investors will choose portfolio B as their risky
  portfolio

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New Facts about Investment and Finance

• There are strategies that results in high average
  returns without large betas
• Investors faced all types of fund styles ---
  value, growth, income, balanced, global, emerging
  market etc
• Returns are predictable at long horizons
• There are other sources of risks priced by the
  market
• So does the traditional advice still holds?

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New Portfolio Theory

• The traditional portfolio theory (or two-fund
  theorem) takes into account two attributes of the
  portfolio to determine optimal asset allocation
• Mean
• Variance
• What about if there are multiple sources of risk.
  For example consider economic downturn or
  recession or low consumption growth rate as an
  additional risk factor

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New Portfolio Theory

• Now investors care about three attributes of
  their portfolio
• Investors want higher average returns
• Investors want lower standard deviations or
  overall risk
• Investors want portfolios that do not perform
  poorly during bad times
• Investors are now willing to accept a portfolio
  with a little lower return or a little higher
  volatility of return if the portfolio does not do
  poorly in bad times

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New Portfolio Theory in Practice

• Basically what the new portfolio theory says is
  that there is an alternative metric for deciding
  whether or not an asset should be added to a
  portfolio for diversification purposes
• One metric is the extent to which an asset
  delivers diversification benefits when most
  needed, i.e in during economic downturns
• So diversification is not just about reducing
  variance while picking up additional returns as
  assets are added

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New Portfolio Theory in Practice

• The paper by Sa-Aadu, Shilling and Tiwari (2006)
  offers one application of the new portfolio
  theory
• We focus on the deterioration consumption growth
  opportunities as the additional risk factor
  investors face
• First, we estimate the benefit of diversification
  induced by addition of various assets to a series
  of diversified portfolios
• Second, we then regress the diversification
  benefit induced by each asset class on two
  measures of investor economic well being
• Third, given good state and bad state of the
  economy we estimated the composition of the
  investor portfolio
• The key finding is the real estate is a good
  hedge in bad times

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REITs are Defensive Assets In addition to
regular Income REITs Hedge Against Economic
Distress
Exhibit 3 Transition Probabilities in Good and
Bad States of Economy
Economy in Good State Economy in Bad State
0.7916 0.6123
Exhibit 4 Optimal Tangency Portfolio
Composition ()
State of Economy Small Cap Stock Large Cap Stock Treasury Bonds Corporate Bonds Commodities and Precious Metals International Equities Equity REITs
Good State 20.45 48.29 0.00 8.16 0.00 23.09 0.00
Bad State 0.00 0.00 36.41 0.00 21.08 0.00 42.51
Source J. Sa-Aadu, Ashish Tiwari and James
Shilling (2006)