Question

c.) Estimating Cost of Carry Factors from Market Data (spreadsheet tab "Carry Analyis") Input information Given the following data: Assume the date is Thursday, January 31, 2020 S&P500 spot = 3,283.66 [SPX INDEX], the index has a dividend yield of 1.81% (compound continuously) S&P500 March 2020 Futures = 3289.75 (maturity 3/20/20) [ESHO INDEX] S&P500 June 2020 Futures = 3,290.00 (maturity 6/19/20) [ESMO INDEX] S&P500 Sept 2020 Futures = 3,289.25 (maturity 9/18/20) [ESUO INDEX] Output Calculate the implied interest rate for the futures contracts relative to the spot value of the S&P500. Use the continuous time formulation for valuing commodity forwards/futures to calculate your answer. Assume the year has 365 days.

Answer 1

Solution:

It is given to assume current date as January 31,2020.

S&P 500 dividend Yield	1.81%
SPX (spot) =	3283.66

Futures contracts	Price	Maturity	Time to expiry in days	Time to expiry in years
ESH0	3289.75	3/20/2020	49	49/365 =	0.1342
ESM0	3290.00	6/19/2020	140	140/365 =	0.3836
ESU0	3289.25	9/18/2020	231	231/365 =	0.6329

Formulas:

Future price =S0(Exp^(r−q)T)

So, Implied interest rate = [ln[Futures price/Spot price] + Dividend yield*T]/T

Calculation:

So, Implied interest rate of ESH0= (ln(3289.75/3283.66)+ (0.0181*0.1342))/(0.1342) =

3.19%

So, Implied interest rate of ESM0= (ln(3290.00/3283.66)+ (0.0181*0.3836))/(0.3836) =

2.31%

So, Implied interest rate of ESU0= (ln(3289.25/3283.66)+ (0.0181*0.6329))/(0.6329) =

2.08%

Final Answer:

Futures contracts	Price	Maturity	Implied Interest rate
ESH0	3289.75	3/20/2020	3.19%
ESM0	3290.00	6/19/2020	2.31%
ESU0	3289.25	9/18/2020	2.08%