Total Return Analysis

Office of Thrift Supervision

Risk Management Division

Anthony G. Cornyn, CFA

Director, Risk Management

Sarah Bryant, Ph.D.

Donald Edwards

Radu Filimon, Ph.D.

Eberhard Irmler

Cezary M. Jednaszewski

Jonathan D. Jones, Ph.D.

Office of Thrift Supervision

1700 G Street, N.W.

Washington, D.C. 20552

Introduction

Last year, both the Federal Financial

Institutions Examination Council

(FFIEC) and the Office of Thrift

Supervision (OTS) issued policy

guidance that recommends institutions conduct a total return analysis

in assessing the effects of interest

rate changes on the returns associated with investment securities and

financial derivatives prior to taking

a position in these financial instruments. The 1998 FFIEC policy

statement states: “The agencies [i.e.,

the FRB, FDIC, OCC, OTS, and

NCUA] agree that the concept of

total return can be a useful way to

analyze the risk and return tradeoffs

for an investment. This is because

the analysis does not focus exclusively on the stated yield to maturity. Total return analysis, which

includes income and price changes

over a specified investment horizon,

is similar to stress testing securities

under various interest rate scenarios.

The agencies’ supervisory emphasis

on stress testing has, in fact, implicitly considered total return.

Therefore, the agencies endorse the

use of total return analysis as a useful supplement to price sensitivity

analysis for evaluating the returns

for an individual security, the investment portfolio, or the entire institution.” In Thrift Bulletin 13a, issued

last year, OTS states: “Management

should exercise diligence in assessing the risks and returns (including

expected total return) associated

with investment securities and

financial derivatives.”

This Risk Management Release discusses total return analysis and

shows how it can be used to measure

the expected return of fixed-income

securities. In evaluating the expected return of an individual fixedincome security, or portfolio of

fixed-income securities, investors

typically use internal rates of return,

such as yield to maturity or yield to

call, as selection criteria. These two

yield measures, however, are unlikely to reflect the correct expected

investment return. Instead, total

return provides a better measure of

prospective investment return.

Conventional

Measures of

Investment Return

The price of a bond is equal to the

present value of the bond’s expected

cash flows. By definition, the yield,

or internal rate of return, is that

interest rate that equates the present

value of a bond’s cash flows to its

current market price. Yield to maturity (YTM) and yield to call (YTC)

are two frequently used measures of

return (or yield) on fixed-income

securities. YTM is used to price and

trade non-callable bonds, while

Risk Management Series

By Jonathan D. Jones, Senior Financial Economist

(202) 906-5729

June 1999
Office of Thrift Supervision

page 2

YTC is used to price and trade

callable bonds.

YTM is the internal rate of return on

a non-callable bond that is held until

maturity. In using this yield measure, one assumes that the security is

held until maturity and that all cash

flows can be reinvested at the same

constant YTM. YTC is the internal

rate of return on a callable bond that

is held until either the first call or

first par call date. In using this yield

measure, one assumes that the security is held until being called by the

issuer and that all cash flows can be

reinvested at the same constant

YTC. 

Both of these return measures have

several important drawbacks. First,

investors typically do not hold

fixed-income investments until

these investments mature or are

called. Second, interim cash flows

cannot be reinvested at the assumed

constant yields. Finally, it is not

possible to compare the likely

returns on investments with different maturities or more complex

return/risk profiles.

Total Return

Analysis in Theory

Total return analysis avoids the

shortcomings associated with using

the two conventional yield measures, YTM and YTC, and provides

an investor with a better measure of

the expected return on fixed-income

investments. The total return (also

known as the horizon or total holding-period return) accounts for the

three sources of potential dollar

return on a bond:

n Coupon interest payments,

n Capital gain or loss when a bond

matures, is sold, or called, and

n Income from reinvestment of

coupon interest payments (interest-on-interest income).

Therefore, to calculate the total

return for a non-callable bond, an

investor chooses an investment horizon or holding period, a reinvestment rate, and a selling price for the

bond at the end of the investment

horizon (i.e., end-of-period required

return). Based on the values chosen

for these parameters, the total return

calculation is straightforward. First,

total coupon payments plus intereston-interest income are calculated for

the assumed reinvestment rate over

the given investment horizon using

the following expression:

where

Coupon plus interest-on-interest =

Coupon

(1+r)

h - 1

r

h = length of investment horizon,

and

r = assumed reinvestment rate.

Second, the predicted sales price of

the bond at the end of the investment

horizon is calculated. Third, total

future dollars derived from the bond

over the holding period are calculated by summing total coupon payments, reinvestment income, and the

predicted sales price. Finally, this

value is substituted into the following expression to obtain the total

return:

y

h

=

Total future dollars

1/h

-1

Purchase price of bond

where r and h are defined as above,

and

Total future dollars =

Coupon payments

+ Interest-on-interest income

+ Sales price.

1

Total Return

Analysis in Practice

There are several different

approaches that could be used to

calculate total return. First, an

investor, or portfolio manager, could

calculate total return on the basis of

subjective forecasts of the reinvestment rate and required yield at the

end of the investment horizon.

Second, implied forward rates from

the yield curve (e.g., U. S. Treasury

or LIBOR yield curves) could be

used to determine the reinvestment

rates and the yield on a bond at the

end of the investment horizon. This

approach to total return analysis

produces what is called an arbitragefree total return because the calculation is based on the market’s

expectations of the reinvestment

rate and end-of-period required

yield. Finally, scenario analysis

could be used to calculate total

return. Scenario analysis involves

specifying different possible values

for the reinvestment rate and the

required yield at the end of a given

investment horizon, and then calculating the total return associated

with each scenario.

Of the three approaches, total return

analysis based on scenario analysis

is the best approach because it

allows an investor, or portfolio manager, to measure how sensitive a

bond’s expected performance is to

1 This discussion draws on material from Frank J. Fabozzi, editor, The Handbook of Fixed Income Securities, 5th Edition, 1997, Chapter 4.

See this chapter for further discussion of the total return concept.
Risk Management Series

page 3

Table 1. Scenario Analysis for Bond A’s Total Return

Required Yield at End of

3-Year Investment Horizon (%)

6.0 8.0 10.0

Reinvestment Rate (%)

4.0 13.36 7.78 3.06

5.0 13.44 7.87 3.16

6.0 13.53 7.97 3.26

The second example compares the

total returns for two bonds of different maturities. The first bond, Bond

A, is the same bond used in the previous example. The second bond,

Bond B, is a 7.25 percent coupon,

14-year non-callable bond with a

current market price of $94.55 and a

yield to maturity of 7.9 percent.

(This example is adapted from

Fabozzi, The Handbook of Fixed

Income Securities, 5th Edition,

pages 72-75.) In comparing the

total returns for the two bonds

below, the investment horizon is set

to three years. On the basis of yield

to maturity, Bond A appears to be a

better investment than Bond B

because of Bond A’s higher yield to

maturity. However, as the example

shows convincingly, yield to maturity is not a reliable measure of

expected investment return. 

Table 1 (left) and Table 2 (page 4)

show various scenarios for the reinvestment rate and end-of-period

required yields for Bond A and

Bond B, respectively. There are

three different reinvestment rates, 4,

5, and 6 percent, and three different

end of period required yields, 6, 8,

and 10 percent. These are the same

values used in the previous example.

The total return estimates for both

bonds vary substantially across the

different rate scenarios. For Bond A,

these estimates range from a maximum value of 13.53 percent to a

minimum value of 3.06 percent. For

Bond B, these estimates range from

a maximum value of 12.16 percent

to a minimum value of 3.48 percent.

This example shows the high degree

of sensitivity of a bond’s expected

return to different values for reinvestment rates and end-of-period

required yields.

If a portfolio manager currently

owned Bond B, the higher yield to

maturity on Bond A might induce

As shown in the tables, there are

three different reinvestment rates, 4,

5, and 6 percent, and three different

end-of-period required yields, 6, 8,

and 10 percent. In both tables, for

each combination of reinvestment

rate and end-of-period yield, there is

a total return estimate for Bond A. 

As shown in the two tables, the total

return estimates vary substantially

across the two investment horizons.

The differences in the total return

estimates illustrate the effect that the

choice of investment horizon has on

a bond’s expected return since the

relative importance of the reinvestment rate and end-of-period

required yield is related to investment horizon. For short investment

horizons, for example, reinvestment

income is small, but it increases in

size as the investment horizon

lengthens. 

differing reinvestment rates and

end-of-period required yields. Total

return analysis can also be used to

compare the expected returns of a

bond for investment horizons of

varying lengths. In the two examples that follow, scenario analysis is

used to compare: (1) the total

returns for a bond using two different investment horizons, and (2) the

total returns for two bonds of different maturities.

To assess the effect on a bond’s total

return of varying the length of the

investment horizon using scenario

analysis, assume a bond, say Bond

A, is a 9 percent coupon, 20-year

non-callable bond with a current

market price of $109.90 and a yield

to maturity of 8 percent. Tables 1

and 1A show various scenarios for

the reinvestment rate and end-ofperiod required yields for Bond A

for a three-year and ten-year investment horizon, respectively. 

Table 1A. Sensitivity of Bond A’s Total Return

to Investment Horizon

Required Yield at End of

10-Year Investment Horizon (%)

6.0 8.0 10.0

Reinvestment Rate (%)

4.0 7.59 6.88 6.24

5.0 7.85 7.16 6.53

6.0 8.11 7.43 6.82
Office of Thrift Supervision

page 4

portfolio of fixed-income securities,

some investors use promised yield

to maturity or yield to call as selection criteria. These yield measures,

however, are unlikely to reflect the

correct expected investment return

as interest rates change and investments are sold prior to maturity.

Instead, total return provides a better

measure of expected investment

return. 

In summary, investment decisions

made on the basis of YTM or YTC

can lead to investments with lower

the manager to swap Bond A for

Bond B in a pure yield pickup swap

transaction. However, Tables 1 and

2 show that the likely returns on

both bonds are sensitive to what

happens to interest rates, despite the

higher promised yield to maturity

for Bond A. To see this more clearly, Table 3 shows the total return for

Bond A minus the total return for

Bond B in basis points.

Table 3 shows that for required

yields of 6 and 8 percent, Bond A’s

total return exceeds that of Bond B’s

for all three reinvestment rates.

However, for a required yield of 10

percent, the situation reverses dramatically, with Bond B’s total return

exceeding that of Bond A. These

results suggest that investment decisions based only on stated yield to

maturity will not produce the best

total returns as interest rates change.

The results of this simple example

demonstrate the importance of conducting a stress test over various

interest rate scenarios when evaluating the expected return on investment securities prior to taking

positions in these financial instruments. 

Conclusion

This Risk Management Release has

shown how total return calculations

based on scenario analysis can be

used to measure the expected return

of fixed-income securities. In evaluating the likely return of an individual fixed-income security, or

Table 2. Scenario Analysis for Bond B’s Total Return

Required Yield at End of

3-Year Investment Horizon (%)

6.0 8.0 10.0

Reinvestment Rate (%)

4.0 12.00 7.50 3.48

5.0 12.08 7.58 3.57

6.0 12.16 7.67 3.67

Table 3. Bond A’s Total Return Minus Bond B’s Total Return

(in Basis Points)

Required Yield at End of

3-Year Investment Horizon (%)

6.0 8.0 10.0

Reinvestment Rate (%)

4.0 136 28 - 42

5.0 137 29 - 41

6.0 137 30 - 41

total returns depending on changes

in reinvestment rates, end-of-period

required yields, and length of the

investment horizon. However, there

is an important caveat. In computing total returns based on scenario

analysis, investors should be aware

that total return estimates will only

reflect expected investment returns

if expectations regarding reinvestment rates and end-of-period yields

turn out to be correct.