The decision on whether to invest in the stock market or in gold can be established by calculating the expected return using probability procedures. Martin (2017) proposes the use of the probabilities and market returns to compute the weighted return in assessing capital investment decision between two or more mutually exclusive project and portfolio for each project of portfolio as follow:
E(R) = ∑ P i R i
Where:
E(R) = Expected return as weighted
∑ = summation
P i = probability of state i
R i = market return for state i
Case 1: Market Expected Return
| State of Economy (i) | Probability (P i ) | Market return (R i ) | Weighted return |
| Boom | 0.15 | 25% | 3.75% |
| Moderate | 0.35 | 20% | 7.00% |
| Weak growth | 0.25 | 5% | 1.25% |
| No growth | 0.25 | (-14%) | -3.50% |
| Expected return for investing in stock market, E(R M ) = ∑ P i R i | 8.50% | ||
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The expected returns from the stock market:
E M = 0.15(.25) + 0.35(.20) +0.25(.5) +0.25(-.14)
= 8.5%
Case 2: Gold Expected Return
| State of economy (i) | Probability(P i ) | Gold Return (R i ) | Weighted return |
| Boom | 0.15 | (-30)% | -4.50% |
| Moderate | 0.35 | -9% | -3.15% |
| Weak growth | 0.25 | 35% | 8.75% |
| No growth | 0.25 | 50% | 12.50% |
| Expected return for investing in gold, E(R G ) = ∑ P i R i | 13.60% | ||
The expected returns from the Gold:
E G =0.15(-.30) + 0.35(-.09) +0.25(.35) +0.25(.50)
=13.60%
From the above computation, it is evident that the expected return on stock market investment is 8.50% while that of investing in Gold is 13.6%. Based on this comparison of the above expected return, it is clear that both investment portfolios have positive expected return. However, Gold has a higher expected return and hence a better choice of investment i.e. E G > E M .
Reference
Martin, I. (2017). What is the Expected Return on the Market?. The Quarterly Journal of Economics , 132 (1), 367-433.
