# Covered Interest Rate Parity

Can someone shed some light on when the covered interest rate parity formula is re-arranged to show a forward premium or discount.

I cannot conceptualize the following text “The domestic currency will trade at a forward premium (Ff/d > Sf/d) if, and only if, the foreign risk-free interest rate exceeds the domestic risk-free interest rate (if > id). The premium or discount is proportional to the spot exchange rate (Sf/d), proportional to the interest rate differential (if – id) between the markets, and approximately propor- tional to the time to maturity (Actual/360)”.

Why would there be a premium if foreign risk-free rate exceeded the domestic risk-free rate?

PG. 494 in CFAI text.

I just read élan on this section few mins ago so this may help yoyou covered interest parity:

F f/d = S f/d x (((1+(Int fc *(actual/360))/(1+(int dc*(actual/360)))

Forward premium (discount) on base or domestic currency

= (F f/d - S f/d) / spot f/d

forward f/c - spot f/c about the same as I fc- I dc

From what I understand, if interest rate partity holds, then it means two things:

• F must equal S*(((1+(Int fc *(actual/360))/(1+(int dc*(actual/360)))
• and ((F f/d - S f/d) / spot f/d approximately = int fc - int dc

In this case, the investor would be indifferent between investing:

• in a ST instrument (eg risk-free rate, LIBOR, deposit rate) of the domestic country at int dc
• or in a ST instrument of the foreign country at int fc, provided that you fully hedge the foreign ccy using a Forward contract in order to convert the foreign ccy back into your domestic ccy.

To the OP - your post shows that domestic currency will trade at a premium (and that would be right when foreign int rate > domestic int rate).

Got it thanks!

A forward premium (for the domestic currency) means that the future exchange rate (f/d) is higher than the spot exchange rate (f/d).

Suppose that the spot rate is 1.3/€, the risk-free rate is 5%, and the € risk-free rate is 2%; the domestic currency is the euro. One year from now, \$1.30 (today) will be worth \$1.30 × 1.05 = \$1.365, €1.00 (today) will be worth €1.00 × 1.02 = €1.02, and the exchange rate will be \$1.365/€1.02 = \$1.3382/€, which is higher than today’s spot rate (\$1.3/€). Thus, a higher foreign risk-free rate (than the domestic risk-free rate) led to a forward premium (for the euro).