Why Discount Factors Usually Decline with Maturity
Summary
The discussion explains why discount factors are often expected to fall as payment dates move further into the future. It frames discounting as valuing later cash flows through successive periods: if each period has a discount factor below one, multiplying the factors makes a more distant payment worth less today. The example uses equal one-year factors to illustrate this compounding effect.
The answer connects increasing discount factors to negative interest rates and explains that the assumption of feasible, risk-free cash deposits at zero interest would rule out investing at a negative rate. That assumption can support a non-increasing discount function. The caveat is that negative rates can occur in actual markets, where investors may accept a charge in exchange for safekeeping or other benefits. The explanation is conceptual; it does not derive a general term-structure result or address details such as collateral conventions, credit risk, or market-specific discount curves.
Key ideas
- Discount factors multiply across periods, so repeated factors below one reduce the present value of more distant payments.
- An increasing discount factor corresponds to negative interest rates under the usual discounting convention.
- If investors can always hold cash at a risk-free zero rate, negative rates would be unattractive under that simplified assumption.
- Negative rates can nevertheless occur when investors accept costs for safety or other services.
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# Why is the discount function non increasing if pure cash holdings are feasible? # Why is the discount function non increasing if pure cash holdings are feasible? I am struggeling with the question, for example lets take a swap with rate of 3.2 for one year and 3.6 for 2 years and Discount Factor 0.96899 for the first year and 0.93158 for the second year. Under the assumption that cash holidings are feasible the Dicount Factor stays the same for the 3rth year if the swap rate is unknown. However this leads me to the quesion: Why is the discount function non increasing if pure cash holdings are feasible? I appreciate your answer! ## Answer by Phil H (score 3, accepted) https://quant.stackexchange.com/a/9534 The essence of discounting is that now is less risky than later. So a contract to deliver £1 in 1 year is more risky than one to deliver £1 tomorrow, (the counterparty could suffer a credit event) so it is worth less. Discount factors multiply; if I know that £1 at 1y is worth £0.98 today, and £1 at 2y is worth £0.98 at 1y (i.e. equal rates for both periods), then that £1 at 2y is worth £1 x 0.98 x 0.98 = £0.9604 today. Increasing discount factors, then, are not impossible, they just imply negative interest rates. I guess the 'pure cash holdings' assumption is that you can always at worst deposit cash at 0% risk-free, so you wouldn't invest in anything with a negative rates; i.e. negative rates wouldn't exist. But in reality negative rates are quite possible, and actually the case in some markets at present. They just indicate that interest rates are low enough and costs of carry high enough that you are charged for the assurance of keeping your money safe, rather than being paid interest to use the money.
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