Computation of Real Investment Rate

Investment Theory
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July 7, 2021
1 Fisher’s equation provides that the Real Interest Rate (RIR) is equal to the Nominal Rate minus the Inflation Rate. Namely,
Real Interest Rate = Nominal Rate – Inflation Rate
Accordingly, the nominal rate could then be derived through transposition, giving us;
Nominal Rate = Inflation Rate + Real Interest Rate
Following this equation, it could be seen that if our RIR remains constant, then a change from 3% to 5% IR would also increase the Nominal Rate.
Aside from the rationale provided above, it must be noted that there is no direct and immediate causation between the rise of inflation Rate (IR) and the decrease in RIR. In real-world applications, there is also the possibility that a rise in the inflation rate will happen during a fall in the nominal rate. Depending on how much the nominal rate would fall, the real interest rate could decrease, remain constant, or even increase.
2 Based on the values provided in the table, the mean and standard deviation could be computed as follows:
1 Mean
E(r ) = [.35 x .445] + [.35 x (-.165)] + [.30 x .14] = .140 or 14%
2 Standard deviation
First we get the variance based on the data
[0.35 (-165 – 14)2] + [.30 (14-14)2] + [.35 (44.5-14)2] = 651.75
Thereafter, we get the square root in order to determine the standard deviation since the latter is just equal to the square root of the former.
Therefore,
SD = √651.75 or 25.52%
3
3 The Real HPR on the bond over the year could be determined through the use of the equation:
r = [(1 + R) / (1-i)] &nd...