The spot price of silver is currently $7.125/oz, while the two- and five-month forward prices are $7.160/oz and $7.220/oz, respectively.
(a) If silver has no convenience yield, what are the implied repo rates?
(b) Suppose silver has an active lease market with lease rate = 0.5% for all maturities
expressed in annualized continously compounded terms. Using the formula developed
in Question 3, identify the implied repo rate for maturities of two months and
five months.
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(a) If silver has no convenience yield, the implied repo rates can be calculated using the formula:
Implied Repo Rate = (F - S) / (S × (t/T))
Where:
F = forward price
S = spot price
t = time to maturity of the forward contract
T = total contract period
For the two-month forward price:
Implied Repo Rate (2-month) = ($7.160 - $7.125) / ($7.125 × (2/12))
= $0.035 / $0.594
= 0.0588 or 5.88%
For the five-month forward price:
Implied Repo Rate (5-month) = ($7.220 - $7.125) / ($7.125 × (5/12))
= $0.095 / $1.484
= 0.064 or 6.4%
(b) If the lease rate is 0.5% for all maturities, the implied repo rate for the two-month and five-month maturities can be calculated using the formula:
Implied Repo Rate = Lease Rate - (F - S) / S
Lease Rate = 0.5% = 0.005
For the two-month maturity:
Implied Repo Rate (2-month) = 0.005 - ($7.160 - $7.125) / $7.125
= 0.005 - $0.035 / $7.125
= 0.005 - 0.0049
= 0.0001 or 0.01%
For the five-month maturity:
Implied Repo Rate (5-month) = 0.005 - ($7.220 - $7.125) / $7.125
= 0.005 - $0.095 / $7.125
= 0.005 - 0.0133
= -0.0083 or -0.83% (negative indicates an arbitrage opportunity)
Therefore, the implied repo rate for the two-month maturity is 0.01% and for the five-month maturity is -0.83%.