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I was talking to a friend recently and he asked me the following question.

If I have a device which perfectly (with 100% accuracy) predicts that both a bond (e.g. AAA rated government bond) and the shares of a listed company (e.g. Google) yield 5% over the next year. If I had US$1 million, which one should I invest in?

Although it seems kind of vague, I'm assuming that I have to sell both instruments after a year to realise the 5% return. My answer was the bond because the a government bond rated at AAA would be very unlikely to go bankrupt (although the country not being bankrupt might be implied by the yield) and bonds are usually less volatile. Further, I at least have a bit of recourse upon default vs shares. Upon giving him the answer, I was told that my answer wasn't totally correct. Does anyone think I'm missing anything? Also is there a way to model this vague question to back up my point of view?

EDIT: Taking into account coupons and dividends, maybe the bond is preferred iff coupon rate > dividend rate. Also, maybe I can forecast the bond YTM. Any ideas will eb appreciated.

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  • $\begingroup$ Sorry, but this question looks a bit off-topic. As a professional you consider coupons, dividends. This should be incorporated in your $5\%$ return with certainty. $\endgroup$
    – Richi Wa
    Jan 5, 2015 at 14:14
  • $\begingroup$ I choose to let it be because it can be viewed as an interview type question where you have to consider what's relevant and what's not. I certainly where you're coming from so I'm interested in the opinion of the rest of the community. $\endgroup$
    – Bob Jansen ♦
    Jan 5, 2015 at 15:35

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I'll assume the rest of the world doesn't have access to a similar oracle. Indeed if it did future returns would converge to the risk free rate instantly.

In this case, I would prefer holding the AAA bond instead of the stock because the rest of the world would consider it to be much less risky.

As a financial institution, reducing the risk of your portfolio as perceived by outsiders is a good idea for many reasons (e.g. to keep regulators happy or to increase investor confidence), but there exists an instantly monetizable advantage which would hold even as a simple individual.

Indeed, assets seen as high quality such as an AAA bond would command a much lower interest rate when used as collateral for borrowing money. In fact, repo-ing out the bond, and using the proceeds to reverse-repo the stock, an arbitrageur initially holding the bond could realize a risk-free profit of roughly $1m * (stock repo rate - bond repo rate) * 1yr. If the bond is a US treasury, its repo rate would be close to fed funds, while the stock's repo rate (if it exists at all) would be more like libor + hundreds of basis points, yielding a profit in the tens of thousands USD.

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  • $\begingroup$ Hi David, that's a great way of looking at it. From what I know, repos are used to raise short term cash by the company issuing them. Am I right in thinking that these would probably not be issued by really profitable companies e.g. Google or only when a companies looking to conduct a relatively significant transaction e.g. M&A and need cash short-term? $\endgroup$
    – Black
    Jan 6, 2015 at 15:36
  • $\begingroup$ I'm not entirely sure what you mean. If the term "repo" is confusing you, here's a simpler way of expressing the arbitrage. What you should do to lock in the profit is borrow 1 million dollars from say bank A, using the bond as collateral, for a low interest rate, and lend that money to say bank B, accepting the stock as collateral, for a higher rate. You would thus lock in the rate differential as profit. The loan to bank B can't default because you know the collateral will appreciate by more than the interest on the loan. Google or other companies are nowhere involved in this. $\endgroup$
    – David Durrleman
    Jan 6, 2015 at 17:25
  • $\begingroup$ @Black Please let me know if this didn't help your understanding, I'd be happy to try and clarify further or expand on another point. Otherwise, and if you agree with my view, do not hesitate to accept my answer so future users can see it as correct :-) Thanks! $\endgroup$
    – David Durrleman
    Jan 8, 2015 at 19:41
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Maybe I'm missing the tricky part of this trick question:

If the device is 100% accurate it doesn't matter as both will yield 5% with certainty. This is the same unless you want to take into account coupons or dividends.

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  • $\begingroup$ Hi Bob, thanks for your input. Yes, that is what I was thinking at first. The yield bit is also confusing because it might mean the total return over the next year. If we take into account the coupons for the bond, I suspect that the bond will be bought iff the coupon rate > dividend rate. Do you agree with this viewpoint? $\endgroup$
    – Black
    Jan 5, 2015 at 11:59
  • $\begingroup$ I'd say that yield should be interpreted as total return here. Always ask for a clear definition of the terms in trick questions ;) Otherwise, I agree. $\endgroup$
    – Bob Jansen ♦
    Jan 5, 2015 at 12:14

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