Making Investment Decisions Using a Decision Tree
Question one
- A Decision Tree
| £2,500 | |||
| Buoyant market = 0.6 | |||
| Moderate market = 0.2 | £500 | ||
| Depressed market = 0.2 | |||
| -£1,000 | |||
| Portfolio of common | |||
| stocks investment | |||
| Fixed-interest | |||
| investment | |||
| £1,200 | |||
- Expected Monetary Value Criterion
Expected monetary value at different market conditions:
Buoyant market = 0.6x£2,500 = £1,500
Steady market = 0.2x£500 = £100
Depressed market = 0.2x -£1,000 = -£200
Total Expected Monetary Value = £1,400
Assuming a risk-neutral investor, the investment which should be chosen is the fixed-interest investment mainly because according to the expected monetary value criterion, the expected monetary value for portfolio in common stocks investment would give £1,400 which is slightly above £1,200 expected from the fixed-interest investment. Thus, since the investor is risk-neutral, it is evident he/she should chose an investment which is relatively risk free.
- The certainty equivalent is a guaranteed return that someone would accept, rather than taking a chance on a higher, but uncertain, return.
- If the certainty equivalent is less than the expected monetary value, the investor is not a risk-taker mainly because he/she chooses an investment with less outcome but certain rather than an investment with a likelihood of high outcome but not certain meaning they is fear of taking risks.
Question two
- A Decision Tree
| £90,000 | ||||||
| When new centre is unsuccessful = 0.2 | ||||||
| When new centre is moderately successful = 0.4 | ||||||
| £70,000 | ||||||
| Established and | When new centre is very successful = 0.4 | |||||
| successful centre | ||||||
| £30,000 | ||||||
| £130,000 | ||||||
| New Centre | Very Successful = 0.4 | |||||
| Moderately Successful = 0.4 | ||||||
| £60,000 | ||||||
| Unsuccessful = 0.2 | ||||||
| £10,000 | ||||||
- Expected Monetary Value Criterion
Established and successful shopping centre:
When the new centre is unsuccessful = 0.2x£90,000 = £18,000
When the new centre is moderately successful = 0.4x£70,000 = £28,000
When the new centre is very successful = 0.4x£30,000 = £12,000
Total Expected Monetary Value = £58,000
New shopping centre:
When the new centre is unsuccessful = 0.4x£130,000 = £52,000
When the new centre is moderately successful = 0.4x£60,000 = £24,000
When the new centre is very successful = 0.2x£10,000 = £2,000
Total Expected Monetary Value = £78,000
Considering the expected monetary value and assuming a risk-neutral decision-maker, it is evident that the shoe store should be located at the new shopping centre because it has a higher total expected monetary value and the operational costs are lower than in the established and successful shopping centre.
- A perfect forecast of shopping centre success would likely change the order of the decision tree in ‘(a)’ mainly because increasing success of the new shopping centre will cause a decrease in the success of the established and already successful shopping centre and vice versa. This means when the new shopping centre is very successful, the established shopping centre becomes unsuccessful. These changes have the potential to significantly change the investment decisions.
Reference
Deng, H., Runger, G. & Tuv, E. (2011). Bias of importance measures for multi-valued attributes and solutions. Proceedings of the 21st International Conference on Artificial Neural Networks (ICANN).
Sung-Hyuk, C. & Tappert, C.C. (2009). A Genetic Algorithm for Constructing Compact Binary Decision Trees. Journal of Pattern Recognition Research, 4 (1): 1–13.
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