What Is a Reinvestment Risk?

Reinvestment risk is the interest income that bondholders receive during the holding period, the principal and interest received at maturity, and the capital gains obtained from the sale. The reinvestment can be achieved with a lower return than the original purchase of the bond. Risk of returns. When interest rates fall, bond prices rise, but the reinvestment yield will decrease, and the risk of reinvestment increases. When interest rates rise, bond prices fall, but interest reinvestment gains rise. Generally speaking, the reinvestment risk of longer maturity bonds and bonds with higher coupon rates is relatively large. The measure to prevent reinvestment risks is to diversify the maturity of bonds and to cooperate in the short and long term. ^[1]

Reinvestment risk

No institutional investor can fully predict the market. For institutional investors, reinvestment risks are especially important. For example, the A project cycle is 20 years, the IRR is 15%, the B project cycle is 2 years, and the IRR is 25%. For institutional investors, Project B may not be better than Project A. Because after the end of the B project, it may rarely exceed 15% in the next 5 years.

The value of investment at risk refers to the reward that investors get when they take risks to invest. The greater the investment risk, the higher the investor's requirements for the return on investment. According to a large number of investment value analysis reports, the value-at-risk of an investment has two forms of expression: the amount of risk reward and the rate of return on risk.

Risk reward

The risk-reward amount is an absolute form of investment risk value, and refers to additional rewards that exceed normal rewards due to risky investments.

Risk return

The risk-return ratio is a relative form of the value-at-risk of an investment, and refers to the proportion of additional returns to the original investment amount.

Calculation of the value of investment at risk

Except for investments in national debt or Treasury bills that are considered to be risk-free, the return on investment for various other investments is generally the sum of the time value of money (interest rate) and the value of investment risk (return on risk). Return on investment = interest rate + value at risk

calculation steps:

In actual work, although the "standard deviation" can reflect the degree of risk taken by an investment project, it is not easy to compare with other schemes, so the "standard deviation rate" needs to be calculated.

1. Determine the various expected returns of the investment project (represented by xi) and their possible probability (represented by pi), and calculate the "expected value" of future returns (represented by \ bar {e} v), and calculate Formula: Expected value of future returns

2. Calculate "standard deviation" (represented by ) and "standard deviation rate" (represented by r).

3. Investment risk value calculation formula: standard deviation rate

4. Determine the "risk factor" (represented by f): Generally, it should be determined according to the attitude of all investors in the industry to risk aversion, which is usually a function of the degree of risk.

5. Introduce risk factor to calculate the expected value of investment risk for the investment plan.

Formula for calculating the value of investment at risk:

Expected return on risk (rpr) = risk factor * standard deviation rate = f *

Expected risk return (rp) = expected value of future returns * expected risk return rate / (time value of money + expected risk return rate)

Compare the expected value of investment risk with the value of investment risk required by the business:

If the expected value of the investment risk> the required value of the investment risk, it means that the risk of the investment plan is large, the return rate is small, and the plan is not feasible. If the expected value of the investment risk is less than the required value of the investment risk, it means that the risk that the investment plan takes is small, the return rate obtained is large, and the plan is feasible.

Calculation of required investment risk value:

Required return on investment = time value of money + required return on risk

Required return on risk = required return on investment-time value of money

Required return on risk = expected value of future returns * required return on risk / (time value of money + required return on risk).