Question

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?

Answer 1

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%

Step-by-step 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.