Another explanation is that longer maturities entail greater risks for the investor (i.e. A risk premium is needed by the market, since at longer durations there is more uncertainty and a greater chance of catastrophic events that impact the investment.This explanation depends on the notion that the economy faces more uncertainties in the distant future than in the near term. More formal mathematical descriptions of this relation are often called the term structure of interest rates.
In addition, lenders may be concerned about future circumstances, e.g.
a potential default (or rising rates of inflation), so they demand higher interest rates on long-term loans than they demand on shorter-term loans to compensate for the increased risk.
The yield for the 10-year bond stood at 4.68%, but was only 4.45% for the 30-year bond.
The market's anticipation of falling interest rates causes such incidents.
This effect is referred to as the liquidity spread.
If the market expects more volatility in the future, even if interest rates are anticipated to decline, the increase in the risk premium can influence the spread and cause an increasing yield.
If investors hold off investing now, they may receive a better rate in the future.
Therefore, under the arbitrage pricing theory, investors who are willing to lock their money in now need to be compensated for the anticipated rise in rates—thus the higher interest rate on long-term investments.
Investing for a period of time t gives a yield Y(t).
This function Y is called the yield curve, and it is often, but not always, an increasing function of t.
Occasionally, when lenders are seeking long-term debt contracts more aggressively than short-term debt contracts, the yield curve "inverts", with interest rates (yields) being lower for the longer periods of repayment so that lenders can attract long-term borrowing.