[eyeC]

Originally Posted by eyeC

Example:
Lets pretend we are back in time trying to value IC property a year ago to see if we should buy or not and we think we know the answer to this question

A studio flat for sale in IC for 240,000AED + 20,000AED expenses associated with the sale (realistic values last year)

Lets assume the three possible economic outcomes are BOOM, NORMAL GROWTH, and RECESSION

Scenario-1-
The market is hot and the economy is booming, prices are rising very fast and we can sell for 400,000 after pocketing one year rent for 40,000 net income.
We give this scenario a low probability of 1:4

Therefore
HPR = (400,000-260,000+40,000)/260,000
HPR (1) =69%

Scenario-2-
Normal growth expected selling price 300,000 and net rent 30,000 we will also assume the probability for this to happen is 50%

Therefore
HPR (2)=27%

Scenario -3-
Worse case scenario prices drop to 200,000 and no one to rent, we will give this a low probability of 1:4

Therefore
HPR (3)= -23%

The reward from the investment is its expected returns which you can think of as the average HPR you would earn if you were to repeat an investment in the asset many times.

The expected return E(r) is the weighted average of returns in all possible scenarios

E(r) =sum { P(S)*R(S)} for s=1,2,3

Where p(s)=probability for each scenario & r(s)=HPR for each scenario

E(r)=0.25*69 + 0.5*27 - 0.25*23=25%
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Expected reward return on the investment=25%
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please refer to table attached

Now of course there is risk to the investment and the actual return may be more or less than 25% if a boom materializes, the return will be better 69%,but a recession ,the return will be negative -23% loss

To quantify the uncertainty of the investment we do the following

The surprise return on the investment in any scenario is the difference between the actual return and the expected return.
For example in a boom (scenario1) the surprise is 69-25=44%

Uncertainty surrounding the investment is functions of the magnitudes of the possible surprises .To summarize risk with a single number we first need to define the variance as the expected value of the squared deviation from the mean.

VAR ( r)=sum { r(s)-E(r)}^2--------------------- equation1

We need to use another term called standard deviation

SD( r)={VAR(r)}^1/2-----------------------equation 2

Applying equations (1) and (2) to find SD(r)

VAR(r )=0.25 * (44)^2 + 0.50 * (2)^2 + 0.25 * (48)^2
VAR( R)=1062

Therefore
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SD( r)=32.5%
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So we now have two results we are going to use later the expected return on the investment and the SD( r)
What do these numbers mean and how do we use them if we want to compare them with other properties or different investments
For this we need to know two more terms risk premiums and risk aversion

To be continued

Risk premiums and risk aversion

-so to invest or not to invest? First we need to ask how much of an expected reward is offered to compensate for the risk involved in the investment.

-we measure the reward as the difference between the expected HPR on the property and the risk –free rate ,that is the rate you can earn by leaving money in risk free assets such as treasury bills ,money markets funds, or bank. The difference is the risk premium. so in our example if the risk –free rate is 6%per year and the expected returns on the property is 25% the risk premium is 19% per year. so it does show its an excellent buy if it was done last year.

Just to give you an idea for stocks the average excess return is 8.5% for the past 70 years

- The degree to which investors are willing to buy the property depends on risk aversion. it seems obvious that investors are risk averse in the sense that if the risk premium were zero , ppl would not be willing to invest any money in the property

-we can repeat the exercise with different inputs lets say a person buying now at current market prices. We need to see how much premium is left for the buyer so that we know if prices have peaked and if it is time to pull out of the investment

-in our simple example you might say the risk premium calculated is quite high at 19% but this is part of the truth we need to discount for the following:

1-time value of money (inflation)
2-intrest rate paid on the original amount
3-depretation on the property lets say expected life span is 20 years discount 1/20th of the original price every year
4-exchange rate
5-return on reinvestment income (positive)

We need to write the risk premium that investor demand of an investment as a function of its risk
Risk aversion=A=risk premium/{1/2 SD(r)^2}

For example the risk-free investments have zero variance, so the investor does not require a risk premium-the return must be equal only to the risk- free rate

Another example for our case if an investor believes the risk premium for the investment is 19% and the standard deviation is 32.5% we could infer risk aversion as

A=0.19/0.5*(0.325)^2
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Risk aversion=A=3.59
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How do we interpret this result?


to be continued