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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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