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Bond Versus Equity When Future Returns Are Certain

Article Quant Q&A · Author: Black
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Summary

The document asks whether an investor should choose an AAA government bond or a company’s shares when both are predicted with certainty to return the same amount over a year. The accepted response favors the bond because other market participants perceive it as safer, which can make it more valuable as collateral. It describes borrowing against the bond through a repo and using the proceeds to finance a stock position through a reverse repo; the difference between their financing rates can create a profit for someone initially holding the bond.

The argument depends on the premise that the rest of the market does not share the hypothetical forecasting ability, so perceived risk and financing terms remain different. It is an illustrative collateral and financing argument, not a complete comparison of investment returns. The document does not quantify practical costs or constraints, and a second response notes that under perfect prediction alone, both investments would have the same certain return, apart from cash flows such as coupons or dividends.

Key ideas

  • Equal predicted returns do not necessarily imply equal collateral value or financing terms.
  • High quality government bonds may support cheaper repo financing than equities.
  • Borrowing against a bond to finance a stock position can exploit a spread between financing rates.
  • The proposed advantage assumes other market participants cannot also predict returns perfectly.
  • Coupons, dividends, financing access, and execution details affect the comparison.

Tags

Fixed incomeEquitiesArbitrageExecution
Full text
# Investment: Bond vs Equity


# Investment: Bond vs Equity












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.

## Answer by David Durrleman (score 3, accepted)

https://quant.stackexchange.com/a/16105

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.

## Answer by Bob Jansen (score 0)

https://quant.stackexchange.com/a/16091

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.