 # Hedged return

IN Assessment- Chung case Q # 6:

The paragraph reads: The expected (local currency) return on the bonds is 8.50 percent, and the 1-year risk-free yields are 1.3 percent in the U.S. and 4.6 percent in Australia. The spot exchange rate is USD0.69/AUD and the one-year forward rate is USD0.67/AUD.

Q: Given the exchange rate and interest rate data provided, if the Australian currency risk is fully hedged, the bond’s expected return will be closest to: A. 3.90%. B. 5.20%. C. 5.60%.

1.3 + 3. 9 = 5.2

B

When given the foward and spot rates you should use those instead of the implied from the yield differences.

Currency return = (0.65/0.67) - 1= -2.9%

Bond Return = 8.5%

Total hedged return = 8.5- 2.9 = 5.6%

I believe both answer are good. (answer B use approximate method, answer C is a exact number)

You won’t get any marks for B.

I agree with June 6th. pokhim, how did you come up with your explantion? I think discount/premium or Id-If are both good.

The differences in yield is the implied forward discount or premium. I calculated it directly from the spot and forward rates that were given in the question.

The answer is mutually exclusive. You can either have B or C. And the answer is C unless S2000 or CPK comes here and tells me otherwise.

Agree C is better.

The approximation is:

8.50% − 4.6% + 1.3% = 5.2%.

The actual hedged return is:

1.085 × 1.013 / 1.046 – 1 = 5.08%.

Well now I just look like a fool…

Also, why don’t we hedge using the forward rate given in the question?.

In fact, we should.

As it turns out, the forward rate is slightly different than what we would get from intersest rate parity. For what it’s worth, it gives a return of 5.4%

If the IRP holds >>> The correct answer would be 8.5% + 1.3% - 4.6% = 5.20%

However, the IRP does NOT hold. Therefore: 8.5% + (0.67/0.69-1) = 5.6%

>>> C

Sorry: Where do you get .67/.69-1? Is the formula:

Domestic Return on Foreign Bond=Local Return on Bond+ (Forward/Spot)-1?

If so, why is the currency return=(Forward/Spot)-1

So the forward rates are a total red herring here? If the prompt asked what the return would be if the hedge was initiated using the current forward rates would the answer then be C?

Foreign returns are not my area of expertise. Let me see if I get this:

1. Hedged Return = local RFR + foreign bond spread

2. Hedged w/ Forwards = local bond return x forward/discount premium

3. Unhedged = local bond return x % change iin Fx spots

1

Approximation = 1.3% + (8.5% - 4.6%) = 5.2%

Exact = 1.085 x (1.013/1.046) = 5.08%

2

Exact = (1.085) * ((0.67/0.69)-1) = 5.35%

If IRP held the forward discount would be equal to @ -2.9% which we should get with equations 1 &2? ((0.67/0.69)-1) = -2.9%. If the question was asking if we should hedge we would do so correct? 5.35% v 5.08%

Hedged Return =

1. Bond Return (foreign) + Forward/discount = 8.5% + (0.67/0.69 - 1) = 5.6% - right answer

(0.67/0.69 is the forward discount that the base currecy, AUD, is trading at)

1. Domestic RF + Country Risk Spread (only if IRP holds) = approximately 1.3% + (8.5% - 2.9%) = 5.2%

Always use 1) unless IRP assumes to hold then 2) can also be used

Unhedged Return =

Bond Return (foreign) + Currency Return

I’m actually more confused now.

Does a hedged return calculation ever use the Forward Rate v the Spot Rate, or only the interest differential?

Forward rate is the rate that you can LOCK IN so it will ALWAYS MATERIALIZE.

On on other hand, the domestic RF + country risk premium is only an APPROXIMATION and will only materialize if IRP holds , which is typically not the case.

Therefore, the Return (foreign currency term ) +/- premium/discount needs to be used if forward rate is given; only use the approximation when forward rate is not given and the interest rate differential is given instead.

^ I believe your answer/ analysis is correct. However, S2000 has different thoughts…what should we do 