# CIIA: How to use discount factors to calculate spot rate

Using discount factors to find the final discount factor in a series

If I already have several discount factors I can use them to calculate the following years’ discount factor; What I need to know is the number of years to maturity, the coupon and the current price.

With those values I can form an equation;

PV = CF or CPN * sum of given discount factors + (FV + final CPN) * x

x = discount factor in the final year

102.72 = 5 * (0.9709 + 0.9335 + 0.8916) + 105 * x

x = 0.8451

Using the discount factor to calculate the spot rate in year 4

Info; required knowledge: 1/(1 + st)t = the discount factor

df4 = 1 / (1 + S4)4 =>

0.8451 = 1 / (1 + x )4 => | * (1 + x )4 | then / [division] by 0.8451

(1 + x )4 = 1 / 0.8451 => | ^1/4 [take the fourth root]

(1 + x ) = (1 / 0.8451)1/4 | calculate right side

1 + x = 1.042973 | subtract 1 , rewrite 0.042973 as %

x = 4.2973% = 4.30%

The discount factor can be used to calculate the spot rate of the same year.

So the above solution answers the question: How do I get the spot rate using the discount factor.

# CIIA: Why is a flexible exchange rate better than a fixed exchange rate?

why-is-a-flexible-exchange-rate-better-than-a-fixed-exchange-rate.pdf

If positive inflation differentials occur and the exchange rate is fixed, the real exchange rate will appreciate. An appreciating exchange rate makes the country less competitive. However a flexible exchange rate acts as a buffer, a shock absorber, an automatic stabiliser. So if the inflation rates change there will be an equivalent change in the nominal exchange rate. This in turn leads to the real exchange rate remaining constant. As we learnt before, a change of the real exchange rate has an impact on the competitiveness of a country.

The price level in the country with the higher inflation will rise. So the nominal exchange rate multiplied with the foreign price level will lead to a higher numerator. However the domestic price level will still be as low as before (denominator). This means the higher numerator divided by the constant denominator will lead to a higher real exchange rate (see formula for real exchange rate)

Relationships:

Fixed exchange rate – no airbag, no shock absorber, no automatic stabiliser.

Real exchange rate moves instead of nominal exchange rate.

Price competitiveness falling (if positive inflation differential)

Price competitiveness rising (if negative inflation differential)

Flexible exchange rate – cushion, automatic stabiliser.

Nominal exchange rate moves, real exchange rate remains constant.

Price competitiveness stable / constant.

Real Exchange Rate:

Sreal = (Snominal * Pf ) / Pd

where

Snominal = nominal spot exchange rate (in American terms) (numerator 1/2)

Pf = foreign general price level in foreign currency (numerator 2/2)

Pd = domestic general price level in domestic currency (denominator (1/1))

Figure: Effect of real exchange rate on current account balance (CB)

# Economics: Uncovered Interest Rate Parity (UIP)

CIIA_Economics_Currency_UIP_Uncovered_Interest_Rate_Parity_Question_Solution

Question setup

In intro text:

„In September 2008 the US Fed fund rate was 2%, while one dollar bought 0.68 Euros.“

In question c)

„…bear in mind that the price of one dollar reached a peak of about 0.80 Euros in November 2008…“

Actual question

1. Briefly present the uncovered interest rate parity (UIRP/UIP) equation, and then assuming that UIRP/UIP holds, exploit it to forecast the three months movement of the USD against the Euro from September to November 2008, bearing in mind that the ECB policy rate (min. bid rate on the main refi operations of the Eurosystem) was 4.25%. What can you conclude about your forecast knowing the USD/EUR movement in the period September-November 2008?

Solution

Note:

Sep 08: One Dollar bought 0.68 Euros = 1 USD = 0.68 EUR

Same as USD/EUR = 1 / 0.68 = 1.4706

Nov 08: One Dollar bought 0.80 Euros = 1 USD = 0.80 EUR

Same as USD/EUR = 1 / 0.80 = 1.2500

Dollar appreciated. (1.4706 – 1.2500) / 1.4706 = 15%

Euro depreciated.

Based on UIRP:

2.25% – 4.50% = -2.25% !!! This value is for a year. We’re looking to forecast the three month movement. So -2.25 * (3/12) = 0.5625% = 0.6%

Move in USD/EUR wasn’t consistent with the interest rate parity equation with respect to the magnitude of the FX move.

Notes:

Problems:

1. Converting a given currency exchange rate
2. Remembering that UIRP (UIP) gives a value for a year; and that period we’re looking at is shorter

Intuition for myself

Sep 08: One Swiss Franc bought 0.826 Euro = 1 CHF = 0.826 EUR

Same as CHF/EUR = 1 / 0.826 = 1.21

Same as EURCHF = 1 / 0.826 = 1.21

Nov 08: One Swiss Franc bought 0.95 Euros = 1 USD = 0.95 EUR

Same as CHF/EUR = 1 / 0.95 = 1.0526

Swiss Franc appreciated.

Euro depreciated.