Suppose you have 1,000 that you can invest in Ted and...

Suppose you have $\$ 1,000$ that you can invest in Ted and Larry's Ice Cream Parlor and/or Ethel's House of Cocoa. The price of a share of stock in either company is $\$ 100$. The fortunes of each company are closely linked to the weather. When it is warm, the value of Ted and Larry's stock rises to $\$ 150$ but the value of Ethel's stock falls to \$60. When it is cold, the value of Ethel's stock rises to $\$ 150$ but the value of Ted and Larry's stock falls to $\$ 60$. There is an equal chance of the weather being warm or cold. a. If you invest all your money in Ted and Larry's, what is your expected stock value? What if you invest all your money in Ethel's? b. Suppose you diversify and invest half of your $\$ 1,000$ in each company. How much will your total stock be worth if the weather is warm? What if it is cold? c. Suppose you are risk-averse. Would you prefer to put all your money in Ted and Larry's, as in part a? Or would you prefer to diversify, as in part b? Explain your reasoning.

Suppose you have $\$ 1,000$ that you can invest in Ted and Larry's Ice Cream Parlor and/or Ethel's House of Cocoa. The price of a share of stock in either company is $\$ 100$. The fortunes of each company are closely linked to the weather. When it is warm, the value of Ted and Larry's stock rises to $\$ 150$ but the value of Ethel's stock falls to \$60. When it is cold, the value of Ethel's stock rises to $\$ 150$ but the value of Ted and Larry's stock falls to $\$ 60$. There is an equal chance of the weather being warm or cold.
a. If you invest all your money in Ted and Larry's, what is your expected stock value? What if you invest all your money in Ethel's?
b. Suppose you diversify and invest half of your $\$ 1,000$ in each company. How much will your total stock be worth if the weather is warm? What if it is cold?
c. Suppose you are risk-averse. Would you prefer to put all your money in Ted and Larry's, as in part a? Or would you prefer to diversify, as in part b? Explain your reasoning.

Key Concepts

Expected Value

Expected value is a fundamental concept in probability and finance that calculates the average outcome of an investment by weighing each possible outcome by its probability. In scenarios with multiple possible states (such as different weather conditions), the expected value provides a single statistic that summarizes what one can anticipate on average over time, even though the actual realized outcome might differ in any individual instance.

Diversification

Diversification involves investing in a variety of assets to reduce risk by not concentrating all funds in a single investment. By spreading investments across companies or asset classes that do not perfectly correlate with each other, an investor can mitigate the impact of any adverse outcome affecting one particular investment. This strategy is employed to smooth out returns and decrease overall portfolio volatility.

Risk Aversion

Risk aversion is an investor’s preference for certainty and minimizing potential losses, even if it means sacrificing some potential gains. Risk-averse individuals tend to favor strategies that reduce variability in returns, such as diversification. In decision-making, risk-averse investors prioritize stability and lower exposure to unfavorable outcomes over the possibility of higher but more volatile returns.

Transcript

0:00 75.

00:02 A venture capitalist, willing to invest $1 million, has three investments to choose from.

00:08 The first investment, a software company, has a 10 % chance of returning $5 million profit, a 30 % chance of returning $1 million profit, and a 60 % chance of losing the million dollars.

00:21 The second company is a hardware company, and it has a 20 % chance of returning $3 million, $40 % chance of returning $1 million and a 40 % chance of losing the million dollars.

00:34 The third company, a biotech firm, has a 10 % chance of winning $6 million profit, a 70 % chance of no profit or loss, and a 20 % chance of losing the million dollars.

00:48 Question a, construct a pdf for each investment.

00:55 So for the software, hardware, and biotech companies, we need to create our, our pdf.

01:02 Each pdf will consist of three x values and their probabilities.

01:10 So for our first pdf we're going to use the software company and instead of writing x i'm just simply going to write s to differentiate between the software hardware and biotech firms.

01:22 For the software company we can either have a five million dollar profit, one million dollar profit or one million dollar loss.

01:29 We know the probabilities of each event is under the five million one million and negative one million and we're going to do this with the hardware and the biotech as well so now for a we have our three pdfs we have our software represented with the s's hardware with the h and the biotech with the b notice that all possibilities are in each pdf with their probabilities given from the problem b find the expected value for each investment the easiest way to do this for each of the three is because we already have the pdf created we can just add in a rough sketch of a third row to multiply each value with its probability so i'm gonna do software we're gonna do s times ps and just multiply straight down i'm also gonna do that for our hardware company so each of our h's times ph same thing with the biotech every b with the probability of those bs so back to the software that 5 million times 10 % ends up being 500 ,000.

03:01 The 1 million with the 30 % ends up being 300 ,000...

Please give Ace some feedback