IPM - Valuation of Bond

30
[email protected] Investment and Portfolio Management Valuation of Bonds Long-term debt securities, such as bonds, are promises by the borrower to repay the principal amount. Notes and bonds may also require the borrower to pay interest periodically, typically semi-annually or annually, and generally stated as a percentage of the face value of the bond or note. We refer to the interest payments as coupon payments or coupons and the percentage rate as the coupon rate. If these coupons are a constant amount, paid at regular intervals, we refer to the security paying them as having a straight coupon. A debt security that does not have a promise to pay interest is referred to as a zero-coupon note or bond. The value of a bond security today is the present value of the promised future cash flows (the interest and the maturity value). Therefore, the present value of a bond is the sum of the present value of the interest payments and the present value of the maturity value. To figure out the value of a bond security, we have to discount the future cash flows (the interest and maturity value) at some rate that reflects both the time value of money and the uncertainty of receiving these future cash flows. We refer to this discount rate as the yield. The more uncertain the future cash flows, the greater the yield. It follows that the greater the yield, the lower the present value of the future cash flows (hence, the lower the value of the bond security). The present value of the maturity value is the present value of a future amount. In the case of a straight coupon security, the present value of the Page 1 of 30

Transcript of IPM - Valuation of Bond

Page 1: IPM - Valuation of Bond

[email protected]

Investment and Portfolio Management

Valuation of Bonds

Long-term debt securities, such as bonds, are promises by the borrower to repay the principal amount.

Notes and bonds may also require the borrower to pay interest periodically, typically semi-annually or

annually, and generally stated as a percentage of the face value of the bond or note. We refer to the

interest payments as coupon payments or coupons and the percentage rate as the coupon rate. If

these coupons are a constant amount, paid at regular intervals, we refer to the security paying them as

having a straight coupon. A debt security that does not have a promise to pay interest is referred to as a

zero-coupon note or bond.

The value of a bond security today is the present value of the promised future cash flows (the interest

and the maturity value). Therefore, the present value of a bond is the sum of the present value of the

interest payments and the present value of the maturity value.

To figure out the value of a bond security, we have to discount the future cash flows (the interest and

maturity value) at some rate that reflects both the time value of money and the uncertainty of receiving

these future cash flows. We refer to this discount rate as the yield. The more uncertain the future cash

flows, the greater the yield. It follows that the greater the yield, the lower the present value of the future

cash flows (hence, the lower the value of the bond security).

The present value of the maturity value is the present value of a future amount. In the case of a straight

coupon security, the present value of the interest payments is the present value of an annuity. Zero

coupon (pure/deep discount) bonds and perpetual (consols) bonds are polar cases of bonds. In the case

of a zero-coupon security, the present value of the interest payments is zero, so the present value of the

bond is the present value of the maturity value. A perpetual bond is a bond issued forever. It has no

maturity period. With a consol the principal amount will not be paid back (it will pay only the interest

amounts).

We can rewrite the formula for the present value of a bond security using some new notation and some

familiar notation. Since there are two different cash flows (interest and maturity value), let C represent the

coupon payment promised each period and M represent the maturity value. Also, let n indicate the

number of periods until maturity, t indicate a specific period, and rd indicate the yield. The present value

of a bond security, V, is given by:

Page 1 of 22

Page 2: IPM - Valuation of Bond

To see how the valuation of future cash flows from bond securities works, let's look at the valuation of a

straight-coupon bond and a zero-coupon bond in the next section.

Valuing a straight-coupon bond

Suppose you are considering investing in a straight-coupon bond that:

promises interest of $100, paid at the end of each year;

promises to pay the principal amount of $1 000 at the end of twelve years; and

has a yield of 5% per year.

What is this bond worth today? We are given the following: interest, C = $100 every year, number of

periods, N = 12 years, maturity value, M = $1,000, and yield, rd = 5% per year.

This bond has a present value greater than its maturity value, so we say that the bond is selling at a

premium from its maturity value. Does this make sense? Yes: The bond pays interest of 10% of its face

value every year. But what investors require on their investment (the capitalization rate considering the

time value of money and the uncertainty of the future cash flows) is 5%. So, what happens? The bond

paying 10% is so attractive that its price is bid upward to a price that gives investors the going rate, the

5%. In other words, an investor who buys the bond for $1 443.17 will get a 5% return on it if it is held until

maturity. We say that at $1 443.17, the bond is priced to yield 5% per year.

2

Page 3: IPM - Valuation of Bond

Suppose, instead, the interest on the bond is $50 every six months (still considered a 10% coupon rate)

instead of $100 once every year. Then, interest, C = $50 every six months, number of periods, N = 12

six-month periods, maturity value, M = $1 000, and yield, rd = 5% per six months.

The bond's present value is equal to its face value and we say that the bond is selling "at par". Investors

will pay face value for a bond that pays the going rate for bonds of similar risk. In other words, if you buy

the 5% bond for $1 000.00, you will earn a 5% annual return on your investment if you hold it until

maturity.

Activity

Suppose a bond has a $1,000 face value, a 10% coupon (paid semi-annually), five years remaining to

maturity, and is priced to yield 8%. What is its value?

4.5.2 Different value, different coupon rate, but same return

How can one bond costing $1 443.17 and another costing $1 000.00 both give an investor a return of 5%

per year if held to maturity? If the $1 443.17 bond has a higher coupon rate than the $1 000.00 bond

(10% versus 5%), it is possible for the bonds to provide the same return. With the $1 443.17 bond, you

pay more now, but also get more each year ($100 versus $50). The extra $100 a year for 12 years

makes up for the $443.17 extra you pay now to buy the bond.

Suppose, instead, the interest on the bond is $20 every year (a 2% coupon rate). Then, interest, C = $20

every year, number of periods, N = 12 years, maturity value, M = $1,000, and yield, rd = 5% per year.

3

Page 4: IPM - Valuation of Bond

The bond sells at a discount from its face value. Why? Because investors are not going to pay face

value for a bond that pays less than the going rate for bonds of similar risk. If an investor can buy other

bonds that yield 5%, why pay the face value ($1 000 in this case) for a bond that pays only 2%? They

wouldn't. Instead, the price of this bond would fall to a price that earns an investor a yield-to-maturity of

5%. In other words, if you buy the 2% bond for $734.11, you will earn a 5% annual return on your

investment if you hold it until maturity.

So, when we look at the value of a bond, we see that its present value is dependent on the relationship

between the coupon rate and the yield. We can see this relationship in our example: if the yield exceeds

the bond's coupon rate, the bond sells at a discount from its maturity value and if the yield is less than the

bond's coupon rate, the bond sells at a premium.

Let's look at another example, this time keeping the coupon rate the same, but varying the yield.

Suppose we have a $1 000 face value bond with a 10% coupon rate, that pays interest at the end of

each year and matures in five years. If the yield is 5%, the value of the bond is given by:

V = $432.95 + $783.53 = $1 216.48.

If the yield is 10%, the same as the coupon rate, 10%, the bond sells at face value:

V = $379.08 + $620.92 = $1 000.00.

If the yield is 15%, the bond's value is less than its face value:

V = $335.21 + $497.18 = $832.39.

When we hold the coupon rate constant and vary the yield, we see that there is a negative relationship

between a bond's yield and its value. This can be illustrated in Table 4.1.

.

Table 4.1

A 10% coupon bond with 5 years to maturity and a has a value is therefore selling

4

Page 5: IPM - Valuation of Bond

yield of ... of ... at ...

5% $1 216.48 a premium

10% $1 000.00 par

15% $ 832.39 a discount

We see a relationship developing between the coupon rate, the yield, and the value of a bond security:

If the coupon rate is more than the yield, the security is worth more than its face value - it sells at

a premium.

If the coupon rate is less than the yield, the security is less than its face value - it sells at a

discount.

If the coupon rate is equal to the yield, the security is valued at its face value.

Let us extend the valuation of bond to securities that pay interest every six-months. But before we do

this, we must grapple with a bit of semantics. In Wall Street parlance, the term yield-to-maturity is used

to describe an annualized yield on a security if the security is held to maturity. For example, if a bond has

a return of 5% over a six-month period, the annualized yield-to-maturity for a year is 2 times 5% or 10%.

But is this the effective yield-to-maturity? Not quite. This annualized yield does not take into consideration

the compounding within the year if the bond pays interest more than once per year. The yield-to-maturity,

as commonly used in Wall Street, is the annualized yield-to-maturity given by:

Annualized yield-to-maturity = rd x 2.

Suppose we are interested in valuing a $1 000 face value bond that matures in five years and promises a

coupon of 4% per year, with interest paid semi-annually. This 4% coupon rate tells us that 2%, or $20, is

paid every six months. What is the bond's value today if the annualized yield-to-maturity is 6%? From the

bond's description, we know that: interest, C = $20 every six months, number of periods, T = 5 times 2 =

10 six-month periods, maturity value, M = $1 000, and yield, rd = 6%/2 = 3% for six-month period. The

value of the bond is given by:

5

Page 6: IPM - Valuation of Bond

If the annualized yield-to-maturity is 8%, then: interest, C = $20 every six months, number of periods, N =

5 times 2 = 10 six-month periods, maturity value, M = $1 000, and yield, rd = = 4% for six-month period,

and the value of the bond is given by:

We can see the relationship between the annualized yield-to-maturity and the value of the 4% coupon

bond in Fig. 4.3. The greater the yield, the lower the present value of the bond. This makes sense since

an increasing yield means that we are discounting the future cash flows at higher rates.

Valuing a zero-coupon bond

The value of a zero-coupon bond is easier to figure out than the value of a coupon bond. Let's see why.

Suppose we are considering investing in a zero-coupon bond that matures in five years and has a face

value of $1 000. If this bond does not pay interest (explicitly at least) no one will buy it at its face value.

Instead, investors pay some amount less than the face value, with its return based on the difference

between what they pay for it and -- assuming they hold it to maturity -- its maturity value.

6

Page 7: IPM - Valuation of Bond

If these bonds are priced to yield 10%, their present value is the present value of $1 000, discounted five

years at 10%. We are given: maturity value, M = $1 000, number of periods, N = 5 years, and yield, rd =

10% per year. The value of the bond security is:

If, instead, these bonds are priced to yield 5%, maturity value, M = $1 000, number of periods, N = 5

years, and yield, rd = 5% per year, and the value of a bond is given by:

The price of the zero-coupon bond is sensitive to the yield: if the yield changes from 10% to 5%, the

value of the bond increases from $620.92 to $783.53. We can see the sensitivity of the value of the

bond's price over yields ranging from 1% to 15% in Fig. 4.4.

7

Page 8: IPM - Valuation of Bond

Activity

1. The XYZ bond has a maturity value of $1 000 and a 10% coupon, with interest paid semi-annually.

(a) If there are five years remaining to maturity and the bonds are priced to yield 8%, what is the

bond's value today?

(b) If there are five years remaining to maturity and the bonds are priced to yield 10%, what is the

bond's value today?

(c) If there are five years remaining to maturity and the bonds are priced to yield 12%, what is the

bond's value today?

2. What is the value of a zero-coupon bond that has five years remaining to maturity and has a yield-

to-maturity of: (a) 6%? (b) 8%? (c) 10%?

Value of a consol bond

Value of a consol is the present value of perpetuity. It is given by:

V= C/rd

Example

Find the present value of a 20%$100 bond issued in perpetuity if the yield rate is 10%.

V=20/0.1=$200

This bond is paying at a premium given that yield rate is lower than the coupon rate.

Yield-to-maturity

The yield-to-maturity is the annual yield on an investment assuming you own it until maturity. It

considers all an investment's expected cash flows - in the case of a bond, the interest and principal. The

8

Page 9: IPM - Valuation of Bond

yield-to-maturity on a coupon bond is the discount rate, put on an annual basis, that equates the present

value of the interest and principal payments to the present value of the bond. In the case of a bond that

pays interest semi-annually, we first solve for the six-month yield, and then translate it to its equivalent

annual yield-to-maturity.

Let's look at yield-to-maturity on a coupon bond. Consider the Acme Corporation bonds with 87/8%

coupon bonds maturing in 2010 and with interest paid-semi-annually, what is the yield-to-maturity on

these bonds if you bought them on January 1, 2000 for 96.5 (which means 96.5% of par value)? Or, put

another way, what annual yield equates the investment of $965 with the present value of the twenty-two

interest cash flows and maturity value?

In this example, we know the following:

V = $1 000 x 96.5% = $965

C = 87/8% /2 x $1 000 = $44.375

M = $1 000

N = 11 years x 2 = 22 six-month periods

and t identifies the six-month period we're evaluating. Therefore,

If V = $965, we have one unknown, rd. Where do we start looking for a solution to rd? If the bonds yielded

87/8%, they would be selling close to par (i.e. $1 000). This would be equivalent to a six-month value of rd

= 8.875%/2= 4.4375% for six months. But these bonds are priced below par. That is, investors are not

willing to pay full price for these bonds since they can get a better return on similar bonds elsewhere. As

a result, the price of the bonds is driven downward until these bonds provide a return or yield-to-maturity

equal to that of bonds with similar risk.

Given this reasoning, the yield on these bonds must be greater than the coupon rate, so the six-month

yield must be greater than 4.4375%. Using the trial and error approach, we would start with 5% and look

at the relation between the present value of the cash inflows (interest and principal) discounted at 5%

and the price of the bonds ($965):

9

Page 10: IPM - Valuation of Bond

In fact, using 5%, we have discounted too much, since the present value of the bond's cash flows using

5% is less than the current value of the bonds. Therefore, we know that rd should be less than 5%. We

now have an idea of where the six-month yield lies: between 4.4375% and 5%. Using a financial

calculator, we find the value of rd = 4.70%, a six-month yield. Translating the six-month yield into an

annual yield, we find that these bonds are valued such that the yield-to-maturity is 9.4%.

Alternatively, the yield to maturity can be approximated using the following formulas:

YTM (rd) =

where p is the rate which results into a bond trade at a premium, i.e. Vp and d is the rate which will result

into a discount value Vd.

OR

YTM (rd) = .

where I is the annual interest payment, Fd is the face or par value of the bond, Vd is market value of the

bond and n is the maturity period of the bond.

Note that the above formulae will not give exact yield but approximate it.

Activity

Suppose a bond with a 5% coupon (paid semi-annually), five years remaining to maturity, and a face

value of $1 000 has a price of $800. What is the yield to maturity on this bond?

Reasons Why A Bond’s Price Will Change

The value of a bond depends on three things; its coupon, its maturity and interest rates. Hence the price

of a bond can change over time for any one of the following reasons.

1. a change in level of interest rates in the economy. For example if interest rates in the economy

increase because of RBZ policy, the price of a bond will decrease, if interest of a bond will rise.

2. a change in the price of a bond selling at a price other than par as it moves toward maturity without

any change in the required yield. Over time the price of a discount bond rises if interest rates do not

change, the price of a premium bond declines over time if interest rates do not change.

3. for a non-treasury security, a change in the required yield because of a change in the yield spread

between non-treasury and treasury securities. If the Treasury rate does not change, but the yield

10

Page 11: IPM - Valuation of Bond

spread between treasury and non-treasury securities, changes (narrows or widens), the price of non-

treasury securities will change.

4. a change in the perceived credit quality of the issuer. Assuming interest rates in the economy and

yield spreads between non-treasury and treasury securities do not change, the price of non treasury

securities will increase if the issuer’s perceived credit quality has improved, the price will drop if the

perceived credit quality deteriorates.

Bond price volatility

The return holding a bond over some time period less than the maturity of the bond is uncertain because

of the uncertainty about the future price of a bond, due to the stochastic nature of future interest rates.

When interest rates rise, the price of bond will fall. Maturity is one of the characteristics of a bond that we

said will determine the responsiveness of a bond’s price to a change in yields. In this section, we

demonstrate this with hypothetical bonds. We will also show other characteristics that influence a bond’s

price volatility and how to measure a bond’s price volatility.

Measure of price volatility: Duration

Participants in the bond market need to have a way to measure a bond’s price volatility in order to

measure interest rate risk and to implement portfolio and hedging strategies. The price sensitivity of a

bond to a change in yield, y, can be measured by taking the derivative of bond price to a change in yield

and then normalizing by the price of the bond. Taking the first derivative of that equation with respect to y

and dividing both sides by P, we get:

where

equation above is called the Macaulay duration of a bond. It is named in honor of Frederick Macaulay

who used this measure in a study published in 1938. Duration is a weighted average term to maturity of

the components of a bond’s cash flows, in which the time of receipt of each payment is weighted by the

present value of that payment. The denominator is the sum of the weights which is precisely the price of

the bond. What makes Macaulay duration a valuable indicator is that as can be seen from equation

above, it is related to the responsiveness of a bond’s price to changes in yield. The larger the Macaulay

duration, the greater the price sensitivity to a bond to a change in yield.

11

Page 12: IPM - Valuation of Bond

The above equation is the formula for a bond that pays interest annually. As the bonds we are discussing

pay interest semiannually, the formula for Macaulay duration must be adjusted to se a semiannual rather

than annual yield and a semiannual interest payment. The number of periods used also should be double

the number of years.

Example

Calculation of Macaulay Duration for a 9%, 5-year Bond Selling at Par

Formula for Macaulay duration:

Information about bond per $100 par:

annual coupon = 0.09 x $100 = $9.00

yield to maturity = 0.09

number of years to maturity = 5 years

price = P = 100

Values adjusting for semiannual payments:

c = $9.000/2 = $4.5

y = .09/2 = .045

n = 5 x 2 = 10

t c

$4.5 4.306220 4.30622

4.5 4.120785 8.24156

4.5 3.943335 11.83000

4.5 3.773526 15.09410

4.5 3.611030 18.05514

4.5 3.455531 20.73318

4.5 3.306728 23.14709

4.5 3.164333 25.31466

4.5 3.028070 27.25262

104.5 67.290443 672.90442

12

Page 13: IPM - Valuation of Bond

Total 100.000000 826.87899

Macaulay duration in six-month periods:

Macaulay duration in years:

Table above shows how Macaulay duration is calculated for the hypothetical 9%, 5 year bond selling at

100 to yield 9%. Notice that we made adjustments to C, y, and n because we assume that the bond pays

interest semiannually. We also divide the Macaulay duration measure given in equation by 2 to convert a

measure given in a semiannual periods to an annual measure.

There are two characteristics that affect the Macaulay duration of a bond, and therefore its price volatility.

First, the Macaulay duration for a coupon bond is less than its maturity. For a zero coupon bond, the

maturity duration is equal to its maturity. Therefore for bonds with the same maturity and selling at the

same yield, the lower the coupon rate, the greater a bond’s Macaulay selling at the same yield, the longer

the maturity, the larger the Macaulay duration and price sensitivity.

The above equation shows how to calculate the percentage change in a bond’s price for a given change

in yield . Bond market participants commonly combine the first two terms on the right hand side of

this equation and refer to this measure as the modified duration of a bond. That is:

Not only is the approximation off, but we also can see that duration estimates a symmetric percentage

change in price, which as we pointed earlier, is not a property of the price/yield relationship for an option-

free bond.

13

Page 14: IPM - Valuation of Bond

A useful interpretation of modified duration can be obtained by substituting 100 basis points into our

equation The percentage price change would then be:

-Modified Duration x (1.00) = -Modified Duration

Thus, modified duration can be interpreted as the approximate percentage price change for a 100 basis

point change in yields. For example, a bond with a modified duration of 6 would change in price by

approximately 6% for 100 basis point change in yield. Institutional investors adjust the duration of a

portfolio to increase (decrease) their interest rate risk exposure if interest rates are expected to fall (rise).

While modified duration measures the percentage price change, the dollar duration of a bond measures

the dollar price change. The dollar duration can be easily obtained given the bond’s modified duration.

For example, if the modified duration of a bond is 5 and its price is 90, this means that its price will

change by approximately $4,5 (5% times $90) for a bonus change in yield.

Notice what happens to duration (steepness of the tangent line) as yield changes: as yield increases

(decreases), duration decreases (increases). This property holds all option free bonds.

Figure – Tangent to Price/Yield Relationship

P*

Y*

Yield

14

Pri

ce

Page 15: IPM - Valuation of Bond

If we draw a vertical line from any yield (on the horizontal axis), the distance between the horizontal axis

and the tangent line represents the price approximated by using duration starting with the initial yield y*.

The approximation will always understate the actual price. This agrees with our illustration earlier of the

relationship between duration and the approximate price change.

For small changes in yield, the tangent line and duration do a good job in estimating the actual price, but

the further the distance from the initial yield, y*, the worse the approximation depends on the convexity

(bowedness) of the price/yield relationship.

Curvature and Convexity

Mathematically, duration is a first approximation of the price/yield relationship. That is duration attempts

to estimate a convex relationship with a straight line (tangent line).

A fundamental property of calculus is that a mathematical function can be approximated by a taylor

series. The more terms a Taylor series uses, the better the approximation. For example, the first two

terms of a Taylor series for the price functioning given by

The fact that duration is the first term of the Taylor series can be seen by comparing the first term on the

right-hand side of the Taylor series requires the calculation of the second derivative of the price function,

equation above. The second derivative of Equation above normalized by price (i.e., divided by price) is:

The measure in equation above when divided by 2 is referred to popularly as the convexity of a bond.

That is:

15

Page 16: IPM - Valuation of Bond

This is unfortunate misuse of terminology because it suggests that the convexity measure conveys the

curvature of the convex shape of the price/yield relationship for a bond. It does not. It is simply an

approximation of the curvature.

Table 17-4

Calculation of convexity for a 9%, 5-year bond selling at par formula for convexity:

Information about bond per $100 par:

Annual coupon = 0.09 x $100 = $9.00

Yield to maturity = 0.09

Number of years to maturity = 5 years

Price = P = 100

Values adjusting for semiannual payments:

C = $9.00/2 = $4.5

y = .09/2 = .045

n = 5 x 2 = 10

t c

$4.5 4.306220 8.6124

4.5 4.120785 24.7242

4.5 3.943335 47.3196

4.5 3.773526 75.4700

4.5 3.611030 108.3300

4.5 3.455531 145.1310

4.5 3.306728 185.1752

4.5 3.164333 227.8296

4.5 3.028070 272.5290

104.5 67.290443 7,401.9440

100.000000 8,497.0650

16

Page 17: IPM - Valuation of Bond

The second term on the right-hand side of equation is the incremental percentage change in price due to

convexity.

For example, convexity for the 5% coupon bond maturing in 20 years is 80.43. Then the approximate

percentage price change due solely to correct for convexity if the yield increases from 9% to 11% (+2.00

yield change) is: If the yield decreases from 9% to 7% (-2.00 yield change),

the approximate percentage price change due solely to convexity would also be 3.22%.

The approximate total percentage price change based on both duration and convexity is found by simply

adding the two estimates. For example, if yields change from 11%, we have a approximate percentage

price change due to:

Duration = -20.80%

Convexity correction = +22%

Total =-17.58%

The actual percentage price change would be –17.94%. for a decrease of 200 basis points, from 9% to

7%, we have an approximate percentage price change due to:

Duration = +20.80%

Convexity correction = +22%

Total =-+24.02%

The actual percentage price change would be +24.44%.

Consequently for large yield movements, a better approximation for bond price movements when interest

rates change is obtained by using both duration and convexity.

Convexity is actually measuring the rate of change of dollar duration as yields change. For all option-free

bonds, modified and dollar duration increase as yields decline. This is a positive attribute of any option

17

Page 18: IPM - Valuation of Bond

fee bond, because as yields decline, price appreciation accelerates. When yields increase, the duration

for all option free bonds will decrease. Once again this is a positive attribute because as yields decline,

this feature will decelerate the price depreciation. This is the reason why we observed that the absolute

and percentage price change is greater when yields decline compared to when they increase by the

same number of basis points. Thus, an option-free bond is said to have a positive convexity.

One final but important note. Duration and convexity are measures of price volatility assuming the yield

curve is initially flat and that if there are any yield shifts they are parallel ones. That is the Treasury yields

of all maturities are assumed to change by the same number of basis points. To see were we assume to

look back at the price function we analysed for changes in yield in equation . Each cash flow is

discounted s the same yield. If the yield curve does not shift in a parallel fashion, duration and convexity

will not do as good a job of approximating the percentage price change of a bond.

Approximating convexity

Ealier formula for approximating duration was presented. An approximation for convexity can be obtained

from the following formula:

using the 5%, 20- year bond, the approximate convexity is:

Security and portfolio analysis

The financial analysis of securities and portfolios can be broadly divided into three broad types of

analysis (with several sub-categories for each broad category): 1) fundamental analysis, 2) technical

analysis, and 3) modern analysis. In the middle, and accepted by all, is "fundamental analysis". At one

end of the spectrum is "modern portfolio theory" which is advocated by "academics". At the other end is

"technical analysis" which is advocated by "technicians" or "chartists". The three types of analysis should

be viewed as complementary and supplemental, as the analyst should be aware of and evaluate every

possible aspect of investments before making decisions or recommendations, giving each the weight it

deserves. Furthermore, analysis can be categorized into five different levels: 1) economy, 2) market, 3)

sector, 4) industry, and 5) firm. Likewise, these five different levels should be viewed as complementary

to each other and all analyzed within the context of the three different types of analysis listed above.

18

Page 19: IPM - Valuation of Bond

Fundamental analysis

"Fundamental analysis" looks at the firm’s "fundamentals": profitability, liquidity, leverage, activity, growth,

market valuation, etc. In the broadest sense, it would include analysis of the economy as a whole (all five

levels apply). The analysis focuses upon (but is not limited to) financial statement analysis. It includes

analyzing categories of financial ratios (as listed above), individual financial ratios, comparative ratio

analysis, common-size analysis, trend analysis, indexed analysis, Du Pont analysis, etc. It views

ownership of common stock as ownership of the firm’s future cash flow stream, earnings, dividends, etc.,

the risk associated with those possible future cash flows, earnings, dividends, etc., and the relative

market valuation of those of a particular firm, industry, sector, or market as a whole relative to other

investment opportunities. It is the most basic type of analysis and the one which is most easily justifiable

(in the opinion of its advocates), regardless of what the other types of analysis might seem to imply (and

especially when they seem to be in conflict with one another). In a sense, it answers the question, "How

much should you pay today, for a dollar (of cash flow, earnings, dividends, etc.) tomorrow?" Phrases

such as, "Let’s look at the ‘fundamentals’" apply to this analysis, and attest to its almost universal

acceptance as "sound" analysis. Almost everyone recognizes and accepts "fundamental analysis", but

some give it more or less weight.

Technical analysis

"Technical analysis" analyzes past market data to explain and predict future market movements. It

focuses upon past price movements (and other factors such as volume, etc.) in an individual stock,

industry, sector, or the market as a whole to determine or derive (or "divine" some would say) either

"patterns" or "conditions" which would give an indication of the future movement in market prices. Its

advocates say: "The best indicator of the market is the market itself." "Don’t tell the market what it should

be, let the market tell you." "Don’t fight the market." "Listen to the market." Its detractors liken this

technique to "reading tea leaves" and finding images in cloud patterns. Its detractors say that it is a

violation of the "efficient market hypothesis (EMH)" and a violation even of the "weak form" of market

efficiency. The primary detractors are academicians who feel it violates accepted academic theory. The

primary proponents are veteran market analysts and technicians who have spent years observing the

market and its patterns. It is the most controversial type of analysis. Without doubt there are elements

which are valid and elements which are invalid, thus the controversy. The wise approach is to take the

"good" aspects and ignore the "bad." The elements which are generally considered valid include analysis

of such things as: 52-week highs and lows, daily highs and lows, 200-day moving averages, 50-day

moving averages, new all-time highs and lows, market volume, advances and declines, short interest,

money flows, etc. The elements which are in wide dispute generally relate to seeing "patterns" in charts

such as: "head and shoulders", "triple-tops", "double-bottoms", etc. In less dispute are patterns such as:

19

Page 20: IPM - Valuation of Bond

"support levels", "resistance levels", "break-outs", "confirmations", etc. At the extreme end of technical

analysis are the "chartists". At the conservative end are the "technical analysts". The elements of

technical analysis which are generally considered valid should be considered as supplementary and

complementary to fundamental analysis and modern analysis and each can be used to support and

confirm the other types of analysis.

Modern analysis

"Modern analysis" or "modern portfolio theory" (or "efficient markets theory" as some may refer to it)

involves the elements of accepted academic theory and mathematical, statistical, and quantitative

analysis. It is broad and includes many elements, but it centres on two elements: 1) that markets are

efficient, and 2) that investments can be evaluated solely in terms of risk and return. Its major advocates

include academicians. Its major detractors include market veterans who view it as so "theoretical" and

"academic" as to be too far removed from the "real world" to be of any great use. Of the three types of

analysis, "fundamental analysis" is too obviously valid to be rejected by anyone who wants to maintain

his/her reputation and be taken seriously. And everyone should accept the soundest elements of

"technical analysis" and "modern portfolio theory" to avoid being rejected as an extremist. But the

extremists of these latter two camps are deeply and strongly divided because each fears that acceptance

of the other must imply rejection of its own technique. For example, a central tenet of “modern portfolio

theory” (MPT) is the “efficient market hypothesis” (EMH). [Indeed, some even refer to MPT as “efficient

market analysis” or simply the “EMH” or some other such related term.] Some MPT advocates

(extremists) view most of all “technical analysis” (especially charting) as a direct violation of the EMH

and, therefore, totally invalid. For them to embrace technical analysis would seem to them to repudiate

modern analysis.

On the other side, the extremists in the "technical analysis" camp, aware of this, cannot accept modern

analysis without repudiating their own techniques. Again, the best elements of all three should be

considered by all, each given the appropriate weight. Extremism is not necessary. "Modern analysis" or

"modern portfolio theory" includes many techniques, the primary ones include the "Markowitz full-

covariance model", the "Sharpe single-index model", and the "(Ross) Arbitrage pricing model". All are

based upon theory and involve mathematical and statistical analysis. Markowitz (perhaps the "father of

modern portfolio theory") focuses upon the asset and portfolio "return" and "risk" based upon the

statistical measures of "mean" and "variance" (the "mean/variance criterion"). It involves mean, variance,

standard deviation, covariance, etc., the "capital market line" (CML), etc. Sharpe can be viewed as an

extension and complement to Markowitz and involves the "capital asset pricing model" (CAPM) and the

"security market line" (SML), the "characteristic line" (CL), etc. Statistically, it revolves around the central

importance of asset and portfolio "beta". The "arbitrage price model" (APM) or "arbitrage pricing theory"

20

Page 21: IPM - Valuation of Bond

(APT) was proposed to "correct" some of the "deficiencies" of the CAPM, but should be viewed as

complementary and supplementary to it, actually, a logical extension of it. "Modern analysis" is not

universally accepted, and its detractors, rather than directly disputing its theoretical and mathematical

bases, simply view it as "moot" and not seminal because it is too far removed from their own "real world"

experience. Its proponents would counter that these detractors simply do not understand the theory and

mathematics involved. Again, all methods should be viewed as supplementary and complementary to

one another, each studied, and each given the weight deserved. The more types of, and levels of,

analysis the analyst is aware of and considers, the more likely the decision-making process will be

improved. 

Financial statement analysis

Although fundamental analysis broadly includes much more, at its heart lies financial statement analysis.

Firms are analyzed by financial statement analysis, while financial statements are analyzed by financial

ratio analysis, and financial ratios are themselves analyzed by methods such as Du Pont analysis, etc.

Technical analysis

Technical Indicators: Technical analysis attempts to explain and predict the market "by itself" based

upon the premise that "price discounts everything" (i.e. since all relevant factors are incorporated in the

price of the stock, the price of the stock is all that must be examined). A study of the market itself (or a

stock itself) may provide useful information. There is no limit to the number of "technical market

indicators" which have been and could be employed. Some are obviously of more or less validity and

acceptance than others. They range from those so obvious that all can agree on, to those so esoteric that

some would liken them to reading tea leaves (e.g. "chartists").

Forms of market efficiency

The degree to which markets are "efficient" (i.e. that markets are "perfect" in that they fully reflect all

relevant information, and that all assets are priced "fairly" and appropriately based upon their true

intrinsic value, and that assets fully incorporate all information) is divided into 3 forms. The 3 forms of

market efficiency are classified based upon the type of information from which an individual could (or

could not, in the case of efficiency) derive "abnormal" profits. The three forms of market efficiency are

detailed in the following sub-sections:

"Weak form" efficiency

Markets fully reflect all information contained in past prices, and therefore no "abnormal" or "excess" or

"economic" profits can be consistently earned by studying past price information. (Seems to imply that

"technical analysis" is invalid, at least in its strictest forms.)

21

Page 22: IPM - Valuation of Bond

“Semi-Strong form” efficiency

Markets fully reflect all information which is publicly available, and therefore no "abnormal" or "excess" or

"economic" profits can be consistently earned by studying publicly available information. (Seems to imply

that "fundamental analysis" is unnecessary.)

"Strong form" efficiency

Markets fully reflect all information, public or private, from any and all sources. (Implies that not even

{illegal} "insider trading" information would be useful.) (Seems to imply, in a narrow sense, that all forms

of analysis: technical, fundamental, and modern, are without necessity, as all assets are perfectly priced

all the time. But, in a broader sense, perhaps some aspects of portfolio theory might still be applicable, as

different investors have different risk profiles.)

Note: The consensus of opinion (at least among academics) is that the stock market is "semi-strong"

form efficient in that it does a reasonably good job of incorporating all publicly available information

immediately.

Activity

Explain the following terms: Technical analysis, fundamental analysis and industrial analysis.

22