A barbell portfolio has more convexity than a laddered portfolio and more convexity than a bullet portfolio (Barbell > laddered > bullet)
Bonds with convexity offer two things:
if interest rates go up, bonds with convexity will lose less in value than “normal” bonds
if interest rates go down, bonds with convexity will gain more in value than “normal” bonds
These two features (i.e. performing less bad when interest rates go up and performing better when interest rates go down)
come at a price --> the price is a lower yield on bonds with convexity.
Under normal market conditions and an upward sloping yield curve, a low volatility environment dominates the landscape. Would you want to have bonds with convexity in a low volatility environment? The answer is no. You would not want this feature that comes at a cost of a lower yield. So a barbell portfolio will underperform under this scenario.
I agree the answer must be the convexity/yield relationship in relation to volatility of spot rates, given normal market conditions (upward sloping yield curve).
In a low vol environment, convexity is cheap. Would this mean the yield advantage for low convexity strategies is low (albeit, admittedly, still an advantage)? If the yield curve was flat and expected to be flat for a long time (lets pretend we are in Japan), would there be no yield advantage from selling convexity?
As for why bullet has higher convexity, it is because there is a non-linear relationship between duration and convexity. If bond A has double the duration of bond B, it will have more than double the convexity.
slightly off topic, I might add that the books say under normal conditions (upward sloping yield curve), the cash flow yield on a portfolio of bonds is higher than the average YTM. If anyone is able to explain why that is so in plain english i’d love to hear it
In low volatility environment, the yield benefit of high convexity bond is close to zero, so instead of buying convexity, you stay neutral or sell any bond with higher convexity you may have in your portfolio.
If the yield curve is expected to be flat, then it make no sense to buy convexity, rather, sell comvexity.