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An investor is analyzing the risk of a possible investment by producing three different scenarios. Under a pessimistic scenario, the property would produce a BTIRRp of 8%; a most-likely scenario would produce a BTIRRp of 12%; and an optimistic scenario would produce a BTIRRp of 16%. The investor assigns the pessimistic scenario a 25% chance of occurring, the most-likely case a 60% chance of occurring, and the optimistic scenario a 15% chance of occurring. What is the standard deviation of the returns?

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Answer:

Scenario    R(%)   P      ER       R - ER    (R - ER)2    (R - ER)2.P

Optimistic   16    0.15   24.0    -17.2      295.84       44.376

Most-likely  12    0.60  7.2       -21,2     449.44        269.664

Pessimistic   8    0.25  2.0      -25.2     635.04        158.760

                                ER 33.2                    Variance    472.80

Standard deviation of the return

= √472.80

= 21.74%

Explanation:

The expected return is the product of return and probability. The total expected return is the aggregate of individual expected return. R - ER is the difference between individual return and total expected return. Variance is (R - ER) raised to power 2 multiplied by probability.

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