Butterfly Spread Yield Curve Impact
Please could someone help me understand the impact of yield curve changes on a long butterfly spread?
Question: If you are long butterfly spread with calls in fixed income securities (assume long 2yr + long 30yr - short 2 x 10yr), what is the impact of:
The butterfly spread increasing?
The curvature increasing?
The curvature decreasing?
Yields in the 2yr + 30yr increasing?
Yields in the 10yr increasing?
Price of 10yr increasing?
I understand the mechanics of a butterfly spread, the concept is simple to understand with stock prices, the long position is designed to have a high probability of earning a limited profit when the future volatility of the underlying asset is expected to be low.
What I have difficulty understanding is the butterfly spreads in fixed income.
From the CFA reading below:
A butterfly long in the wings and short in the body is long (has positive) convexity and benefits from volatile interest rates. This butterfly also benefits from a yield curve flattening (unrelated to its convexity).
So a long butterfly spread (2yr + 30yr - 2 x 10yr) profits from a flatter yield curve. How does this relate to the actual butterfly spread? Correct my if I’m wrong - as I understand it if a curve flattens, yields in the 2yr + 30yr increase (or 10yr yields decrease) then their respective call prices will be reduced (10yr price increased) which in turn will reduce the butterfly spread - so a decrease in the butterfly spread is equivalent to a decrease in curvature i.e. spread = curvature?
So a long butterfly spread profits from the spread decreasing? Intuitively that sounds wrong - if I’m long the spread I would expect to profit from the spread going up.
What confuses the matter for me is that the scenario I’ve described above is a “positive butterfly”.
Also how does convexity feature in this?
I’ve used the following references:
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