To calculate the credit valuation adjustment (CVA) for the forward contract, we need to determine the expected loss due to the counterparty default risk. The expected loss is the product of the probability of default, the notional amount of the contract, and the expected loss given default (ELGD):

Expected Loss = Probability of Default * Notional Amount * ELGD

First, we need to calculate the notional amount of the contract. Let’s assume the fund manager has entered into a forward contract to buy 100 ounces of gold. Therefore, the notional amount of the contract is $180,000.

Next, we need to determine the ELGD. The ELGD is the expected loss given that the counterparty has defaulted. In this case, the expected recovery rate is 30%. Therefore, the ELGD is 1 – 30% = 70%.

Now we can calculate the expected loss:

Expected Loss = 2% * $180,000 * 70% = $2,520

The expected loss represents the expected reduction in the value of the forward contract due to the counterparty default risk. Therefore, to adjust for this risk, we need to subtract the expected loss from the value of the forward contract:

CVA Adjustment = Expected Loss * e^(-rT) * N(-d2)

where r is the riskless rate, T is the time to maturity of the contract (1 year), and d2 is the standard normal cumulative distribution function of -d1, where d1 is given by:

d1 = [ln(S0/K) + (r + σ^2/2)T] / (σ*sqrt(T))

where S0 is the current forward price, K is the strike price, σ is the volatility of the forward price, T is the time to maturity, and ln is the natural logarithm.

Using the given values, we have:

S0 = $2000
K = $1800
r = 5% per annum
σ = 25%
T = 1 year

Therefore,

d1 = [ln(2000/1800) + (0.05 + 0.25^2/2) * 1] / (0.25 * sqrt(1)) = 0.747

and

d2 = -0.153

Using the standard normal cumulative distribution function, we get N(-d2) = 0.5596.

Therefore,

CVA Adjustment = $2,520 * e^(-0.05*1) * 0.5596 = $1341.42

Finally, to determine the value of the forward contract after the adjustment, we subtract the CVA adjustment from the current forward price:

Value of Forward Contract = $2000 – $1341.42 = $658.58 per ounce

Therefore, the total value of the forward contract is $658.58 * 100 ounces = $65858.