Newsletter #167
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It's Hard to Distinguish Skill from Luck
Seven Quantitative Insights into Active Management - A Summary
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Risk Manager 2.0
The Market Impact Model™ - Part 3
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Ron Kahn Looks
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The BARRA Brainteaser
for Summer 1998
Solution to the Spring
1998 Brainteaser
A Beautiful Mind
Solution to the Spring 1998 Brainteaser
By Eugene ReznikBrainteaser from Spring 1998
It’s a little-known fact that, next to solving crimes, Sherlock Holmes’s favorite hobby was investing. An inquisitive Dr. Watson once asked Holmes about his fixed income portfolio. “Elementary, my dear Watson—elementary!” exclaimed the grand master. “I hold only three bonds. All of them mature in an integral number of years. As for the exact dates, you can deduce them yourself: The product of the bonds’ maturities (in years) is 36, and the sum is equal to the number of cases I have solved this year.”
After a moment’s contemplation, Holmes added: “Ah—I really have not given you sufficient information. You should also know that the longest bond has a semi-annual coupon.”
Help Dr. Watson deduce the maturities of the three bonds in Holmes’s portfolio.
Solution
The first piece of information given to Dr. Watson is that the product of the bonds’ maturities (in years) is 36. Immediately, the methodical Watson comes up with the 8 possible values for the maturities of the bonds (see table 1).
The second clue Holmes gives Watson is that the sum of the bonds’ maturities equals the number of cases Holmes has solved. Before Holmes leaves the bewildered Dr. Watson to ponder the question, he realizes that even if his colleague were able to recall the number of cases Holmes had solved he would not be able to uniquely determine the maturities of the bonds in question. This implies that the bonds’ maturities must add up to 13, since this is the only value that would not yield a unique set of maturities. Dr. Watson can thus use the deductive techniques he has learned from Holmes to conclude that the final clue implies that the maturities of the bonds must be either 1,6,6 or 2,2,9. Holmes’ allusion to a “longest” bond isolates 2,2,9 as the only possible answer.
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Table 1
