Sensitivity Analysis Bonds:

Even if a bond is finally redeemed at the promised nominal value (usually 100% of its face value), the price of it is subject to fluctuations during its lifetime.
These price fluctuations are in direct negative correlation with the development of the (secondary) market yield for this sort of bond. If the market yield for this type of security increases (for example because the risk assessment made by market participants has deteriorated, or because the central bank’s key interest rate increased), the market price of already existing bonds of this type will decrease, until they feature the same market yield. Because the coupon of bonds is usually fixed, it is only possible to achieve the same higher market yield till final maturity for a new sale through a price reduction of the existing bond traded in the secondary market.

This means de facto that bond prices decrease when the level of secondary market yields for this type of bond (type = comparable issuer/risk class/duration) rises. This price decrease is all the more considerable as the duration of the bond increases. The duration classifies the average capital lockup period in the bond, measured in years. The duration is above all determined by the remaining maturity of the bond – the longer the remaining maturity of the bond, the higher the duration of the bond and therefore the heftier the price decrease of the bond during an increase of the secondary market yield level. A common German government bond with five years until final maturity has for example usually a duration of about four years, one with ten years left has usually a duration of about 8 years.

In addition, with the help of an example the sensitivity of the market price (rate) of a bond to a change of (secondary) market yields and furthermore increasing duration will be shown.

Example:
The table shows the resulting price decrease of a bond (starting from a price of 100%) from every combination of the duration of a bond and a given increase of secondary market yield levels. For the decrease of the secondary market yield level, the same sensitivity applies as shown in the table, only in this case the price of this bond increases by the same amount instead of decreasing.
Table 1: new price of a government bond, starting from 100%, for a given increase of secondary market yield levels (in percentage points) dependent on the duration of the bond.
Specific example:

If for example, like shown in the table above, the secondary market yield level for a bond with a duration of 5 years (column 5) increases by 0.5 percentage points (row 5), the market price of this bond will decrease by about 2.5% (difference between the new market price of about 97.5 vs. the original price of 100%).
Typical reasons why the secondary market yield level should increase are for example an improvement of the economic outlook, the expectation that key interest rates will be increased in the near future by the central bank or even the fact that the central bank is actually increasing key interest rates.
The secondary market yield level for a specific bond type can also increase, if the market’s risk assessment for this specific type of bond (for example Greek government bonds with a duration of about 5 years) deteriorates. In this case, the market will demand a higher yield to compensate for the higher risk it feels these papers entail. The secondary market yield level will increase accordingly as the market price of current bonds drops. Here, the same sensitivity numbers as presented in the previous table apply.

Sensitivity Analysis Credit

The prices of credit instruments (corporate bonds, bank bonds, covered bonds and similar credit instruments) are subject to certain price fluctuations during maturity until repayment.
Prices of credit instruments are subject to similar laws as risk-free (government) bonds, however the (higher) credit risk (i.e. the risk that an issuer cannot fulfil its obligations towards creditors) has a greater influence on the price determination mechanism, and all the more so, the weaker the credit rating or the higher the risk premium. The extent of the credit risk is (in technical terms) a function of 1) the likelihood that an issuer will be unable to meet its obligations (= probability of default) and 2) the monetary loss in the event of such default (= 100% minus the recovery rate).
The following example shows the probability of default (PD) for a credit instrument (here with a five-year maturity and an assumed recovery rate of 40%), depending on the amount of the risk premium. If the probability of default rises, market participants also require a higher risk premium to compensate for the increased risk, and vice versa.

Cumulated 5 j default probability
Price fluctuations of credit instruments are therefore directly connected with the yield development (which consists of the risk-free interest rate with equivalent maturity and the risk premium (yield spread)). The weaker the rating of a credit instrument, the higher the influence of a change in the risk premium on the price determination, i.e. the share of the risk premium in the yield is very high in such cases. The stronger the credit rating of a credit instrument (as priced by market participants), the less dependent is the price development on the change in risk premium – then it depends rather on the development of risk-free government bond yields (a kind of "risk-free" pricing benchmark).

The duration of a credit instrument denotes the average period over which capital of a credit instrument is tied up (measured in years) and can be used for the approximation of the price change in case of small yield changes. For credit instruments with high changes in risk premiums it is recommended that one takes into account also the convexity measure, because the present value of credit instruments (and of other fixed-income securities associated with credit risks) is convex in the case of interest rate changes and yield changes can often be substantial. Convexity takes into consideration this curvature (and is the second derivative of the price function with respect to the yield), and is thus a more accurate approximation of the actual change in value. A high convexity is usually desirable as it indicates that the price of a credit instrument falls less pronounced, given rising yields, and in the case of declining yields the price advances stronger than for credit instruments with lower convexity.

Example:
The example below shows the change in price over one year for a credit instrument with five-year residual maturity, coupon of 7% p.a., price of 100% with a risk premium of 5% and an assumed maturity equivalent risk-free yield of 2%. The values in the table show the expected price changes for such a credit instrument and take into account the duration as well as the convexity effect in the case of varying risk premium or risk-free yields.
If the risk premium increases, for example, within one year by 2 percentage points and the maturity equivalent risk-free interest rate (usually German government bond yield) climbs by 0.20 percentage points, the price decreases from 100% to 92.904%. Taking into account coupon of 7% accrued over this period, this results in an expected total return ([92.904 + 7] / 100) of -0.10%.
Here it should be noted that with the increase in risk premium from 5% to 7% the priced default risk (see table "Cumulative 5-year probabilities of default") has risen, too.