An active United States–based credit manager faces the following US and European investment-grade and high-yield corporate bond portfolio choices:
| Rating Category | OAS | EffSpreadDur | Expected Loss |
|---|---|---|---|
| USD IG | 1.25% | 4.50 | 0.40% |
| USD HY | 3.00% | 5.50 | 2.25% |
| EUR IG | 1.15% | 4.75 | 0.50% |
| EUR HY | 3.25% | 6.00 | 2.50% |
The EUR IG and EUR HY allocations are denominated in euros, and the euro is expected to depreciate by 2% versus the US dollar over the next year.
Question
Q.
What is the approximate unhedged excess return to the United States–based credit manager for an international credit portfolio index equally weighted across the four portfolio choices, assuming no change to spread duration and no changes to the expected loss occur?
- A.–0.257%
- B.–0.850%
- C.0.750%
Solution
A is correct. We solve for the excess spread by subtracting Expected Loss from the respective OAS:
| Rating Category | OAS | EffSpreadDur | Expected Loss | E(Excess Spread) |
|---|---|---|---|---|
| USD IG | 1.25% | 4.5 | 0.40% | 0.85% |
| USD HY | 3.00% | 5.5 | 2.25% | 0.75% |
| EUR IG | 1.15% | 4.75 | 0.50% | 0.65% |
| EUR HY | 3.25% | 6 | 2.50% | 0.75% |
Recall that the United States–based investor must convert the euro return to US dollars using RDC = (1 + RFC) (1 + RFX) – 1, so the USD IG and USD HY positions comprising half the portfolio return an average 0.80%, while the EUR IG and EUR HY positions return –1.314% in US dollar terms (= ((1 + ((0.65% + 0.75%)/2)) × 0.98) – 1), so –0.257% = ((0.80% – 1.314%)/2).
Can anyone explain why we are unable to weight each index spread by 25% and the math doesn’t work? When I see equally weighted across four portfolios, I’m contributing 25% to each… why does this not work?