A venture capitalist, willing to invest $1,000,000, has three investments to choose from.

Question

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars.

Part (a)

1. Construct a PDF for each investment.
2. Software company:

x P(X = x) x · P(X = x)

$5,000,000
$1,000,000
−$1,000,000

1. 
   
2. Hardware company:

x P(X = x) x · P(X = x)

$3,000,000
$1,000,000
−$1,000,000

1. 
   
2. Biotech firm:

x P(X = x) x · P(X = x)

$6,000,000
0
−$1,000,000

Part (b)

1. Find the expected value for each investment.

software company	$
hardware company	$
biotech firm	$

Part (c)

1. Which is the safest investment? Why do you think so?
2. The first investment is safest because there is a 10% chance of making $5,000,000.
3. The third investment is safest because in the long run, the risk of losing any money is the least.    
4. The second investment is safest because there is a 60% chance of making money, which is higher than with the first and third investments.
5. The second investment is safest because it has the greatest expected value.

Part (d)

1. Which is the riskiest investment? Why do you think so?
2. The third investment is the riskiest because it has the greatest chance of not returning any money or losing money.
3. The third investment is the riskiest because it only has a 10% chance of returning any money.    
4. The first investment is the riskiest because it has the greatest chance of losing money and the lowest expected value.
5. The second investment is the riskiest because there is a 40% chance of making $1,000,000 and a 40% chance of losing $1,000,000, so the result would be no change in the investment.

Part (e)

1. Which investment has the highest expected return, on average?
2. software company
3. hardware company
4.     biotech firm

Answer 1

1. Software company:

x P(X = x) x · P(X = x)

$5,000,000	.1	$500,000
$1,000,000	.3	$300,000
−$1,000,000	.6	-$600,000

1. 
   
2. Hardware company:

x P(X = x) x · P(X = x)

$3,000,000	.2	$600,000
$1,000,000	.4	$400,000
−$1,000,000	.4	-$400,000

1. 
   
2. Biotech firm:

x P(X = x) x · P(X = x)

$6,000,000	.1	$600,000
0	.7	$0
−$1,000,000	.2	-$200,000

Part (b)

1. Find the expected value for each investment. To find it, for each investment, add the values of x·P(x) for the 3 possible outcomes.

software company	$ 200,000
hardware company	$ 200,000
biotech firm	$ 400,000

c. The third investment is safest because in the long run, the risk of losing any money is the least. 

1. d. The first investment is the riskiest because it has the greatest chance of losing money and the lowest expected value.

e. As calculated in Part B, the biotech firm produces the highest expected return.