14. Quiz: Applied Standard Deviation and Variance
Investment Data
Consider we have two investment opportunities:
| Returns | ||||||
|---|---|---|---|---|---|---|
| Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | |
| Investment 1 | 5% | 5% | 5% | 5% | 5% | 5% |
| Investment 2 | 12% | -2% | 10% | 0% | 7% | 3% |
The returns for 6 consecutive years for each investment are shown above. Use this information to answer the questions below.
Start Quiz:
What is the average return on investment 1? (Write your answer as a percentage without a percent sign. For example, 9% should be reported as 9, or 93% should be reported as 93.)
SOLUTION:
5Start Quiz:
What is the average return on investment 2? (Write your answer as a percentage without a percent sign. For example, 9% should be reported as 9, or 93% should be reported as 93.)
SOLUTION:
5Investment Data
In the previous two questions, you should have found that these investments have the same mean! That is, regardless of which investment opportunity you choose, you are expected to earn the same amount. So how are they different? Let's look at some additional questions to see if we can find some differences.
The same data as above is provided again (to minimize scrolling).
| Returns | ||||||
|---|---|---|---|---|---|---|
| Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | |
| Investment 1 | 5% | 5% | 5% | 5% | 5% | 5% |
| Investment 2 | 12% | -2% | 10% | 0% | 7% | 3% |
The returns for 6 consecutive years for each investment are shown above. Use this information to answer the questions below.
SOLUTION:
- The risk associated with investment 1 is lower than the risk associated with Investment 2.
- The standard deviation associated with Investment 1 is smaller than the standard deviation associated with Investment 2.
SOLUTION:
Investment 2Useful Insight
The above example is a simplified version of the real world, but does point out something useful that you may have heard before. Notice if you were not fully invested in either Investment 1 or fully invested in Investment 2, but instead you were diversified across both investment options, you could earn more than either investment individually. This is the benefit of diversifying your portfolio for long term gains. For short term gains, you might not need or want to diversify. You could get lucky and hit short term gains associated with the upswings (12%, 10%, or 7%) of Investment 2. However, you might also get unlucky, and hit a down term and earn nothing or even lose money on your investment using this same strategy.