Warren Buffy is an enormously wealthy investor who has built his fortune through his legendary investing acumen. He currently has been offered three major investments and he would like to choose one.

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The first one is a conservative investment that would perform very well in an improving economy and only suffer a small loss in a worsening economy. The second is a speculative investment that would perform extremely well in an improving economy but would do very badly in a worsening economy. The third is a countercyclical investment that would lose some money in an improving economy but would perform well in a worsening economy.

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Warren believes that there are four possible scenarios over the lives of these potential investments: $(1)$ an improving economy, $(2)$ a stable economy, $(3)$ a worsening economy, and $(4)$ a pandemic economy. He is pessimistic about where the economy is headed, and so has assigned probabilities of $0\mathrm{.}1,0\mathrm{.}4,0\mathrm{.}3,0\mathrm{.}2$ respectively, to these four scenarios. He also estimates that his profits $($in millions of dollars$)$ under these respective scenarios are those given by the following table:

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Economy

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Investment Type

Improving

Stable

Worsening

Pandemic

Conservative

$$30$

$$5$

$-$$$10$

$-$$$10$

Speculative

$$40$

$$10$

$-$$$30$

$-$$$40$

Countercyclical

$-$$$5$

$$5$

$$15$

$$20$

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Which investment should Warren make under each of the following criteria?

$($a$)$ Maximin strategy. Please state$/$indicate the value of the worst case scenario for each possible choice in addition to the optimal choice.

$($b$)$ Maximax strategy. Please state$/$indicate the value of the best case scenario for each possible choice in addition to the optimal choice.

$($c$)$ Expected monetary value $($EMV$)$ criteria.

$($d$)$ Perform sensitivity to investigate the change in investment decision when the probability of Stable Economy is traded with probability of Improving Economy. Consider changes in the probability of Stable Economy from $0\mathrm{.}1$ to $0\mathrm{.}5.$

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Hint: To trade probabilities on the spreadsheet, set the probability of Improving $=1-($the sum of the other three probabilities$).$ That way when the probability of Stable Economy changes $($decreases say$)$ so will the probability of Improving Economy $($increases by the same amount$)$ while keeping the same probabilities for Worsening and Pandemic Economies. Note that the sensitivity analysis investigation is in the range for which the total sum of probabilities remains $1.$ Warren Buffy is an enormously wealthy investor who has built his fortune through his legendary investing acumen. He currently has been offered three major investments and he would like to choose one.

The first one is a conservative investment that would perform very well in an improving economy and only suffer a small loss in a worsening economy. The second is a speculative investment that would perform extremely well in an improving economy but would do very badly in a worsening economy. The third is a countercyclical investment that would lose some money in an improving economy but would perform well in a worsening economy.

Warren believes that there are four possible scenarios over the lives of these potential investments: $(1)$ an improving economy, $(2)$ a stable economy, $(3)$ a worsening economy, and $(4)$ a pandemic economy. He is pessimistic about where the economy is headed, and so has assigned probabilities of $\backslash (0\mathrm{.}1,0\mathrm{.}4,0\mathrm{.}3,0\mathrm{.}2\backslash )$ respectively, to these four scenarios. He also estimates that his profits $($in millions of dollars$)$ under these respective scenarios are those given by the following table:

Which investment should Warren make under each of the following criteria?

$($a$)$ Maximin strategy. Please state$/$indicate the value of the worst case scenario for each possible choice in addition to the optimal choice.

$($b$)$ Maximax strategy. Please state$/$indicate the value of the best case scenario for each possible choice in addition to the optimal choice.

$($c$)$ Expected monetary value $($EMV$)$ criteria.

$($d$)$ Perform sensitivity to investigate the change in investment decision when the probability of Stable Economy is traded with probability of Improving Economy. Consider changes in the probability of Stable Economy from $0\mathrm{.}1$ to $0\mathrm{.}5.$

Hint: To trade probabilities on the spreadsheet, set the probability of Improving $\backslash (=1-\backslash )($the sum of the other three probabilities$).$ That way when the probability of Stable Economy changes $($decreases say$)$ so will the probability of Improving Economy $($increases by the same amount$)$ while keeping the same probabilities for Worsening and Pandemic Economies. Note that the sensitivity analysis investigation is in the range for which the total sum of probabilities remains $1.$ Show how to do it in excel