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Cash flow duration, like effective duration, considers the change in the cash flow due to prepayment with the change in the interest rate. In effective duration, cash flows are calculated using the Monte Carlo method, but in cash flow duration the cash flows are calculate using static methodology. Following are the steps followed to calculate cash flow duration:
Cash flows are calculated based on some prepayment assumptions.
Using the calculated cash flows and the market price (P0), the cash flow yield is computed.
Cash flow yield is then increased by Δ y and the new prepayment rate at that higher cash flow yield is determined from a prepayment model. The prepayment rate would be lower because of the higher yield.
Using this lower prepayment rate, we can arrive at cash flow and the value of the cash flow using the higher cash flow yield as the discount rate (P+).
Similarly, cash flow yield is decreased by Δy and the new payment rate at lower cash flow yield is calculated. Then, using this higher prepayment rate, cash flow and the value of the cash flow using the lower cash flow yield as the discount (P-) is calculated.
Once we calculate P+ and P-, we can calculate the duration using the general formula of duration i.e.,
Duration =
When we compare modified duration, effective duration and cash flow duration, modified duration is considered inferior to that of cash flow duration. This is because modified duration ignores the changes in prepayment due to interest rate changes. Cash flow yield is based on naïve assumption about how prepayments may change; in contrast, Monte Carlo simulation model is based on more sophisticated analyses of how the cash flow can change when interest rates change. The effective duration computed using Monte Carlo method is considered superior to cash flow duration.
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