1. A town relies on four different sources for its non-drinking water needs: dam water, reclaimed water, rain water, and desalinated water. The different sources carry different risks and costs. For instance, desalinated water is fully reliable due to abundant sea water, but it is more expensive than other options. Reclaimed water also has relatively lower risk than rain or dam water since a certain amount can be obtained, even during the dry. season, by the treatment of daily generated waste water. Using any of the four options requires an investment in that resource. The return on a particular water source is defined as the amount of water generated by the source per dollar of investment in it. The expected returns and standard deviations of those returns for the four water sources are described in the following table: Water resource Expected return St. Deviation Dam water 2.7481 0.2732 Reclaimed water 1.6005 0.0330 Rain water 0.5477 0.2865 Desalinated water 0.3277 0.0000 Higher returns are desirable, but higher standard deviations expose the town to a water crisis. The town needs to decide how to allocate its budget among the different sources to increase the return on water generation while mitigating its risk. The correlation coefficients between dam water and reclaimed/rain water are given below: Dam water Reclaimed water Rain water 0.253 0.232 It is assumed that the correlation between the returns on rain water and reclaimed water is zero. (a) Use Markowitz portfolio selection theory to argue that the optimal relative propor- tions invested in dam, rain and reclaimed water are the same, irrespective of how the town balances higher expected returns against higher standard deviations. Find those proportions. (Hint: this is akin to finding the optimal efficient portfolio).
1. A town relies on four different sources for its non-drinking water needs: dam water, reclaimed water, rain water, and desalinated water. The different sources carry different risks and costs. For instance, desalinated water is fully reliable due to abundant sea water, but it is more expensive than other options. Reclaimed water also has relatively lower risk than rain or dam water since a certain amount can be obtained, even during the dry. season, by the treatment of daily generated waste water. Using any of the four options requires an investment in that resource. The return on a particular water source is defined as the amount of water generated by the source per dollar of investment in it. The expected returns and standard deviations of those returns for the four water sources are described in the following table: Water resource Expected return St. Deviation Dam water 2.7481 0.2732 Reclaimed water 1.6005 0.0330 Rain water 0.5477 0.2865 Desalinated water 0.3277 0.0000 Higher returns are desirable, but higher standard deviations expose the town to a water crisis. The town needs to decide how to allocate its budget among the different sources to increase the return on water generation while mitigating its risk. The correlation coefficients between dam water and reclaimed/rain water are given below: Dam water Reclaimed water Rain water 0.253 0.232 It is assumed that the correlation between the returns on rain water and reclaimed water is zero. (a) Use Markowitz portfolio selection theory to argue that the optimal relative propor- tions invested in dam, rain and reclaimed water are the same, irrespective of how the town balances higher expected returns against higher standard deviations. Find those proportions. (Hint: this is akin to finding the optimal efficient portfolio).
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter17: Long-term Investment Analysis
Section: Chapter Questions
Problem 2.4CE
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Transcribed Image Text:1. A town relies on four different sources for its non-drinking water needs: dam water,
reclaimed water, rain water, and desalinated water. The different sources carry different
risks and costs. For instance, desalinated water is fully reliable due to abundant sea water,
but it is more expensive than other options. Reclaimed water also has relatively lower
risk than rain or dam water since a certain amount can be obtained, even during the dry.
season, by the treatment of daily generated waste water.
Using any of the four options requires an investment in that resource. The return on a
particular water source is defined as the amount of water generated by the source per
dollar of investment in it. The expected returns and standard deviations of those returns
for the four water sources are described in the following table:
Water resource
Expected return St. Deviation
Dam water
2.7481
0.2732
Reclaimed water
1.6005
0.0330
Rain water
0.5477
0.2865
Desalinated water
0.3277
0.0000
Higher returns are desirable, but higher standard deviations expose the town to a water
crisis. The town needs to decide how to allocate its budget among the different sources
to increase the return on water generation while mitigating its risk.
The correlation coefficients between dam water and reclaimed/rain water are given below:
Dam water
Reclaimed water Rain water
0.253
0.232
It is assumed that the correlation between the returns on rain water and reclaimed water
is zero.
(a) Use Markowitz portfolio selection theory to argue that the optimal relative propor-
tions invested in dam, rain and reclaimed water are the same, irrespective of how
the town balances higher expected returns against higher standard deviations. Find
those proportions. (Hint: this is akin to finding the optimal efficient portfolio).
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