Ipm - Valuation Of Bond

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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:

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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.

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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.

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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 yield of ... 5% 10% 15%

of ... $1 216.48 $1 000.00 $ 832.39

at ... a premium par 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.

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•

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:

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:

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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.

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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.

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Activity 1. The XYZ bond has a maturity value of $1 000 and a 10% coupon, with interest paid semiannually. (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 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 8 7/8% 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:

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V

=

C

=

$1 87/8%

M

000 /2

x x

=

96.5% $1

$1

=

000

=

$965 $44.375

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 r d = 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):

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) = p +

Vp V p + Vd

× (d − p )

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.

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OR

Fd − Vd ) n . Fd + 2Vd 3

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

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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:

dp 1 1 = D dy p 1 + y where

(1)C (2)C (3)C (n)(C + M ) + + + ... + 2 3 (1 + Y ) (1 + Y ) (1 + Y ) (1 + Y ) n D= p 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. 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:

(1)C (2)C (3)C (n)(C + M ) + + + ... + 2 3 (1 + Y ) (1 + Y ) (1 + Y ) (1 + Y ) n p Information about bond per $100 par:

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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

c (1.045) t

t×

1 2 3 4 5 6 7 8 9 10

$4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 104.5

4.306220 4.120785 3.943335 3.773526 3.611030 3.455531 3.306728 3.164333 3.028070 67.290443 100.000000

4.30622 8.24156 11.83000 15.09410 18.05514 20.73318 23.14709 25.31466 27.25262 672.90442 826.87899

Total

C (1.045) t

(1)C (2)C (3)C (n)(C + M ) + + + ... + 2 3 (1 + Y ) (1 + Y ) (1 + Y ) (1 + Y ) n = 826.87899 p

Macaulay duration in six-month periods:

Macaulay duration in years:

826.87899 = 8.27 100

8.27 = 4.13 2

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.

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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.

dp 1 =− D(dy ) p (1 + y ) The above equation shows how to calculate the percentage change in a bond’s price for a given change in yield (dy ) . 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:

mod ified duration =

Macaulay Duration (1 + y )

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 optionfree 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.

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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.

Price

Figure – Tangent to Price/Yield Relationship

P*

Y* Yield 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

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dP dP 1 1 d 2P 1 2 = dy + dy P dy p 2 dy 2 p 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:

(1)(2)C (2)(3)C (3)(4)C (n)(n + 1)(C + M ) + + + ... + 2 3 (1 + Y ) (1 + Y ) (1 + Y ) d P1 (1 + Y ) = 2 2 dy p (1 + Y ) P 2

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

convexity =

1 d2p 1 2 dy 2 p

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:

(1)(2)C (2)(3)C (3)(4)C (n)(n + 1)(C + M ) + + + ... + 2 3 (1 + Y ) (1 + Y ) (1 + Y ) (1 + Y ) n (1 + Y ) 2 P 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

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y = .09/2 = .045 n = 5 x 2 = 10 t 11 12 13 14 15 16 17 18 19 20 21

c

c (1.045) t

$4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 104.5

4.306220 4.120785 3.943335 3.773526 3.611030 3.455531 3.306728 3.164333 3.028070 67.290443 100.000000

t (t + 1)

c (1.045) t

8.6124 24.7242 47.3196 75.4700 108.3300 145.1310 185.1752 227.8296 272.5290 7,401.9440 8,497.0650

(1)(2)C (2)(3)C (3)(4)C (n)(n + 1)(C + M ) + + + ... + 2 3 (1 + Y ) (1 + Y ) (1 + Y ) (1 + Y ) n (1 + Y ) 2 P The second term on the right-hand side of equation is the incremental percentage change in price due to convexity.

Percentage change in price due to to correction for convexity = convexity × (change in yield ) 2 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: 80.43 × (+0.02) 2 = 3.22%. 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%

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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 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:

approximating convexity =

P+ + P− − 2 P0 2 P0 (∆y ) 2

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

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approximating convexity =

63.8593 + 62.5445 − 2(63.1968) 2(63.1968)(.001) 2

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. 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

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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: "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.

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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 fullcovariance 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" (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

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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.) “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.

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