Slides MFI Chap. 2

Júlio Lobão

66

Faculdade de Economia do PortoMaster in Finance

Money Market

Characteristics:- trading of short-term securities that are usually very liquid (close to the notion of money)- traded securities:

- have a low default risk- are usually bought and sold in large denominations- have maturities that range from one day to one year (more

often three months or less)- electronic trading- secondary markets are very active for most of the instruments- because of the high amounts traded, the main market participants are central banks, commercial banks, treasuries and large firms

2. Financial Investments2.1. Money market instruments

Júlio Lobão

67


Purpose of the money markets: manage short-term cash needs (liquidity)

In theory, commercial banks could replace the money markets in the task of managing liquidity:- they have a better knowledge of the clients’ characteristics- can benefit from efficiency gains when processing information

But the existence of the money markets can be justified:- commercial banks have to comply with regulatory requirements and pay several costs

- e.g., minimum reserve requirements, solvability and capital ratios)- commercial banks have some advantages when dealing with asymmetric information problems

- when those problems are not serious, the costs are the most relevant issue


Júlio Lobão

68


The investments in money market securities do not produce high returns but, nonetheless, the returns are higher than those of the alternative investments (bank deposits).

Money markets enable to reduce the opportunity costs of having very liquid assets.- most of the trading (more than 90%) have maturities less than amonth

The investments in the money market are mainly caused by precaution issues:- mutual funds- treasuries- firms in the process of liquidation


Júlio Lobão

69


Money market participants:

1) Governments (treasuries)- management of the taxes cycle- issue Treasury Bills

2) Central banks- open market operations in order to control the economy’s money supply- management of the yield curve

- suggestion: take a look at the dynamic yield curve

3) Commercial banks- issue deposit certificates and repurchase agreements (repos)- hold the greatest part of the debt securities issued by the treasuries- manage the liquidity and trade on clients’ behalf


Júlio Lobão

70


4) Large firms- relevant because they issue most of the commercial paper

The individual investors can access the money markets via money market mutual funds- mutual funds pool the resources of many individual investors and purchase money market securities on their behalf


Júlio Lobão

71


Interbank money market- subset of bank-to-bank money transactions that take place in the money market

The euro-zone money market is increasingly indexed to the reference rate euro overnight index average (EONIA)- overnight trades with no collateral- 49 European banks


0,000

0,100

0,200

0,300

0,400

0,500

0,600

0,700

0,800

0,900

1,000

04/01

/2010

18/01

/2010

01/02

/2010

15/02

/2010

01/03

/2010

15/03

/2010

29/03

/2010

12/04

/2010

26/04

/2010

10/05

/2010

24/05

/2010

07/06

/2010

21/06

/2010

05/07

/2010

19/07

/2010

02/08

/2010

16/08

/2010

30/08

/2010

13/09

/2010

27/09

/2010

11/10

/2010

Júlio Lobão

72


Instruments traded in the money markets:

1) Treasury Bills (T-Bills):- the most marketable of all money instruments- maturities up to one year- issued below par (discount from the stated maturity value)- with no default risk- with low inflation-risk (unexpected inflation changes) because of the short-term maturity- very liquid secondary market with low transaction costs- during the last years, treasuries have been issuing bills with longer maturities (role of the financial crisis)


Júlio Lobão

73


2) Commercial paper

- issued by large, well-know companies- minimum maturity varies from country to country (from one day to two years)- usually issued below par- good alternative to the bank loans (lower costs)- used as bridge financing

- temporary loan that will eventually be replaced by a more permanent financing

- usual in events such as a merger or acquisition- secondary market is not very relevant

- buy-and-hold strategy is the most common- national markets remain separated (large differences in the

fiscal and legal framework)


Júlio Lobão

74


3) Certificates of Deposit (CD)

- security issued by a bank- represent a deposit with a specific rate of interest and maturity date- can be bought / sold before the maturity date- the investor who holds the deposit certificate at the maturity date gets the capital and interest (similar to bonds)- maturity usually from one to 4 months- the interest rate is slightly higher than the treasury bill’s rate (reflecting a superior default risk)


Júlio Lobão

75


4) Repurchase agreements (repos)

- sale of securities (e.g., treasury bills) together with an agreement to buy back the same securities at a later date by a price agreed in advance.- usually it is a short-term agreement, from 1 to 14 days, although it can reach 3 months- very safe in terms of credit risk because the loans are backed by the securities- the monetary authorities (e.g., ECB) buy/sell securities to thecommercial banks with a repurchase agreement taking place usually 2 weeks later

- it is a short-term loan with a collateral- agents can manage liquidity and profit from changes in interestrates


Júlio Lobão

76


5) Eurodollars

- dollars-denominated deposits at foreign banks or foreign branches of American banks- these banks are not regulated by the Federal Reserve- most are of deposits less than 6 months’ maturity- are used by the banks as an alternative to the loans made by the monetary authorities- the banks may buy/sell overnight amounts denominated in dollars- in the London market, those amounts are traded at the LIBID (London Interbank Bid Rate) and at the LIBOR (London Interbank Offer Rate) rates- it is an highly competitive market


Júlio Lobão

77


The interest rates of the all these securities tend to move in the same direction at the same time and by similar amounts- short-term securities with low risk and are traded in a competitive market (close substitutes)


OPEC I

OPEC II

87 market crash

LTCM

Subprime mortgagecrisis

Júlio Lobão

78


A. Key concepts:

Bond: security that is issued in connection with a borrowing arrangement- the borrower issues (i.e., sells) a bond to the lender for someamount of cash- the issuer makes specified payments to the bondholder at specified dates

Coupon: payments of interest to the bondholder for the life of the bond

Par value (or face value): repayment of the debt to the bondholder when the bond matures

Coupon rate: it determines interest payment- the annual payment equals the coupon rate times the bond’s par value

2. Financial Investments2.2. Bonds

Júlio Lobão

79


Bond market- it is one of the capital markets where investors trade long-term securities (maturities longer than 1 year)- issuers sell securities to obtain long-term financing- the market participants are the households, the firms and the treasuries- there has been efforts to harmonize the bond markets of the euro-zone (e.g., trading platforms) in order to create a homogeneous market- the fixed-income bonds are the most important in the market- several bond maturities:

- treasuries issue bonds with maturities from 1 to 30 years- corporate issues have shorter maturities typically


Júlio Lobão

80


B. Types of Bonds:

1) Treasury bonds- finance the public debt- have no default risk but have interest rate risk (role of the inflation)- the USA government issues T-Bills (maturities up to 1 year), T-notes (maturities up to 10 years) and T-Bonds (from 10 to 30 years)- represent the most important segment of the bond market

- more than 50% in the euro-zone- securities used in open market operations- very active secondary market, with high liquidity- some treasuries have been issuing inflation-indexed bonds

- e.g., USA, France, Italy, Greece, United Kingdom, Sweden


Júlio Lobão

81


1) Treasury bonds- prior to the current crisis, the differences between the bond returns issued by the euro-zone countries have somewhat been reduced:

- the expectation of variations in the exchange rate has ended as a risk factor

- the fiscal treatment of treasury bonds has been harmonized

- there are still some risk factors such as the credit risk and the liquidity risk


Júlio Lobão

82


2) Corporate bonds- private firms borrow money directly from the public- the risk and promised return depend on the probability of default- in the euro-zone, the bonds issued by banks are very important- the European bond markets have become increasingly integrated during the last years- many institutional investors no longer have restrictions about investing in foreign bonds since the introduction of the euro- firms and treasuries compete for financing resources in the market- there are still some important barriers to market development

- information problems concerning the corporate bond segment

- the corporate bond segment is less liquid- lack of hedging instruments- economic growth is cyclical and that affects the market


Júlio Lobão

83


Callable bonds: allow the issuer to repurchase the bond at a specified call price before the maturity rate- if a company issues a bond with a high coupon rate when the market interest rates are high, and then the interest rates fall, the firm may want to redeem the bond before the maturity date in order toreduce its interest payments- to compensate investors for the risk, callable bonds are issued with higher coupons than noncallable bonds

Puttable bonds: gives the option to the bondholder to extend or retire the bond- if the bond’s coupon rate is lower than current market yields, for instance, the bondholder will choose to reclaim the principal which can then be invested at (more favourable) current yields


Júlio Lobão

84


Convertible bonds: give bondholders an option to exchange each bond for a specified number of shares of common stock of the firm- conversion ratio gives the number of shares for which each bondmay be exchanged

Floating-rate bonds: have a variable coupon that is equal to a money market reference rate plus a quoted spread- e.g., current T-bill rate (or euribor rate) plus 0.2%

Asset-backed bonds: the income from a specified group of assets is used to service the debt

Indexed bonds: make payments that are tied to a general price index or the price of a particular commodity- e.g., Treasury Inflation Protected Securities (TIPS) issued by the US Treasury- the interest rate on these bonds is a risk-free real rate


Júlio Lobão

85


3) International bonds

Foreign bonds: issued by a borrower from a country other than the one in which the bond is sold- the bond is denominated in the currency of the country in which is marketed- e.g., dollar-denominated bond sold by a German firm in the US

Eurobonds: issued in the currency of one country but sold in other national markets- e.g., Eurodollar, i.e., dollar-denominated bonds sold outside the US (not just in Europe)


Júlio Lobão

86


C. Bond Pricing

To value a security, we have to discount its expected cash flows by the appropriate discount rate

Bond value = Present value of coupons + Present value of par value

with a constant coupon we have then

whereT: maturity rater: discount rate


( ) ( )∑= +

++

=T

tTt r1

Value Parr

Coupon Value Bond1 1

( )( )T

T

rvalue Par

rrCoupon Value Bond

++⎥

⎦

⎤⎢⎣

⎡ +−=

−

11*11*

Júlio Lobão

87


For example, for a 30-year maturity bond with a par value of 1000€, semiannualcoupon payments and a coupon rate of 8%- then this bond pays 60 semiannual coupon payments of 40€ each- if the market interest rate is also 8% annually (i.e., r = 4% per six-month-period)

Because, in this example, the coupon rate equals the market interest rate:

If the interest rate were not equal to the bond’s coupon rate, the bond would not sell at par value.


( )( )60

60

%411*1000

%4%411*40

++⎥

⎦

⎤⎢⎣

⎡ +−=

−

Value Bond

( )( )

Pricevalue ParValue Bond ===+

+⎥⎦

⎤⎢⎣

⎡ +−=

−

1000%41

1*1000%4

%411*40 60

60

Júlio Lobão

88


The bond price will rise (fall) as market interest rates fall (rise).- present value of bond’s payments is obtained by discounting at a higher interest rate- interest rate fluctuations represent the main source of risk in the bond market


Bond price at given market interest rate

0

500

1000

1500

2000

2500

3000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Interest rate (%)

Bon

d pr

ice

(€)

Júlio Lobão

89


An important property of bond prices: convexity- The shape of the curve implies than an increase in the interest rate results in a price decline that is smaller than the price gain resulting from a decrease of equal magnitude in the interest rate- the price curve becomes flatter at higher interest rates- i.e., progressive increases in the interest rate result in progressively smaller reductions in the bond price


Bond price at given market interest rate

0

500

1000

1500

2000

2500

3000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Interest rate (%)

Bon

d pr

ice

(€)

Júlio Lobão

90


The longer the maturity of the bond, the greater the sensitivity of its price to fluctuations in the interest rate- the longer the period which the bondholder’s money is tied up, the greater the loss (gain) caused by a rise (fall) of the interest rate- this is why the short-term treasury bills are considered the safest asset

- no default risk and low interest rate risk


Júlio Lobão

91


D. Bond Yields

1) Yield to maturity- the discount rate that makes the present value of the bond’s payments equal to its price- measure of the average rate of return that will be earned on a bond if it is bought now and held until maturity- standard measure of the total rate of return

For example, the yield to maturity of a 8% coupon, 30-year bond selling at 1276.76€ would be the rate r in the equation:

Solution: r = 3% per half-year, or 6.09% per year (compound interest)


( )( )60

60

1100011*4076.1276

rrr

++⎥

⎦

⎤⎢⎣

⎡ +−=

−

Júlio Lobão

92


The bond’s yield to maturity is the internal rate of return on an investment in the bond- can be interpreted as the compound rate of return over the life of the bond under the assumption that all bond coupons can be reinvested at that yield

Yield to maturity depends only on the bond’s coupon, current price, and par value at maturity- can be easily calculated

You may use the function of Excel to calculate the yield to maturity:

= YIELD (settlement date, maturity date, annual coupon rate, bond price, redemption value as percent of par value, number of coupon payments per year)


Júlio Lobão

93



Source: Mauldin and Tepper (2011)

Júlio Lobão

94


2) Current yield- annual coupon divided by bond price- may differ from the yield to maturity

For this bond, which is selling at a premium over the par value (1276.76€ rather than 1000€), the coupon rate (8%) exceeds the current yield (6.27%) which exceeds the yield to maturity (6.09%)

The yield to maturity accounts for the built-in capital loss on the bond (we buy for 1276.76€ something that at maturity will be worth only 1000€)

For premium bonds (i.e., price > par value), the coupon rate is higher than the yield to maturity

For discount bonds (i.e., price < par value), the relationship is reversed


year per yield Current %27.676.1276

80==

Júlio Lobão

95


3) Yield to call

When interest rates fall, the present value of the bond’s scheduled payments rises, but the call provision allows the issuer to repurchase the bond at call price

At high market interest rates, the values of the straight and callable bonds converge

At very low market rates, the bond is called so its value is simply the call price


The blue line is the value at various market interest rates of a “straight” (i.e., noncallable) bond

Interest rate

It is the yield of the bond if you were to buy and hold the security until the call date

Júlio Lobão

96


It is more important to calculate the bond’s yield to call rather than its yield to maturity if the bond is likely to be called

The yield to call is calculated just like the yield to maturity except that the time until call replaces time until maturity and the call price replaces the par value

Example: a 8% coupon, 30-year maturity bond sells for 1150€ and is callable in 10 years at a call price of 1100€. Its yield to maturity and yield to call would be calculated using the following inputs:


Yield to call Yield to maturityCoupon payment 40€ 40€Number of semiannual periods 20 periods 60 periodsFinal payment 1100€ 1000€Price 1150€ 1150€Annual Yields (effective) 6.5% 6.94%

Júlio Lobão

97


E. Bond Prices over Time

A bond will sell at par value when its coupon rate equals the market interest rate- the investor receives fair compensation for the time value of money in the form of the coupon payments- no further capital gain is necessary to provide fair compensation

But, when the coupon rate is lower than the market interest rate, the coupon payments alone will not provide investors the same return they could earn elsewhere in the market- investors also need to earn price appreciation on their bonds- the bonds would have to sell below par value to provide a “built in”capital gain on the investment


Júlio Lobão

98


Example: a bond was issued several years ago when the interest rate was 7% so the bond’s coupon annual coupon rate was set at 7%- the bond pays its coupon annually- now, with three years left in the bond’s life, the interest rate is 8% per year

The bond’s fair market price is the present value of the remaining annualcoupons plus payment of par value:

In another year, after the next coupon is paid, the bond would sell at

So, the total return over the year would equal the coupon payment plus capital gain, or 70 + (982.17 – 974.23) = 77.94

The rate of return would be exactly the current rate of the market:


( )( )

23,974%81

1*1000%8

%811*70 3

3

=+

++− −

( )( )

17,982%81

1*1000%8

%811*70 2

2

=+

++− −

%823,97494,77

=

Júlio Lobão

99


When bond prices are set according to the present value formula, any discount (premium) from par value provides an anticipated capital gain (loss) that will augment (reduce) a below (above)-market coupon rate enough to provide a fair total rate of return

As the bond approach maturity, they will converge to the par value because fewer of these below or above-market coupons remain.


Júlio Lobão

100


To summarize, each bond offers investors the same rate of return- although the capital gain versus income components may differ- if not, investors will try to sell low-return securities thereby driving down the prices until the total return at the now lower price iscompetitive with other securities


Júlio Lobão

101


Holding-period return is the rate of return over a particular period and depends on the market price of the bond at the end of that holding period

When the yield to maturity is unchanged over the period, the rate of return on the bond will equal that yield as we have seen

But when yields fluctuate, so will a bond’s rate of return- unanticipated changes in market rates will result in unanticipated bond returns and, because of that, a bond’s holding period return can be better or worse than the yield at which initially sells

Example: a 30-year bond paying an annual coupon of 80€ and selling at par value of 1000€; the initial yield to maturity is 8%- afterwards, if it falls below 8% the bond price will increase; suppose the price increases to 1050€


( ) %8%131000

1000105080>=

−+= return period-Holding

Júlio Lobão

102


An increase (decline) in the bond’s yield to maturity acts to reduce (increase) its price, which means that the holding-period return will be less (greater) than the initial yield


Júlio Lobão

103


F. Default risk and bond pricing

Default risk: is the investor’s risk of loss arising from a bond’s issuer who does not make payments as promised

Bond default risk is measured by rating agencies such as Moody’s, Standard & Poor’s and Fitch


Moody’s Standard & Poor’s Fitch

Aaa AAA AAA Prime: capacity to pay interest and principal isextremely strong

Aa AA AA High grade: capacity to pay interest andprincipal is very strong

A A A Upper medium grade: capacity to pay interestand principal is strong

Baa BBB BBB Lower medium grade: capacity to pay interestand principal is adequate

Ba BB BB Non-investment grade / speculative

B B B Highly speculative

Caa CCC CCC Substantial risks / extremely speculative / indefault with little prospect for recovery

C D D In default

Júlio Lobão

104


Bond indenture- there are conflict of interests between the bondholders and thestockholders- it is the contract between the issuer and the bondholder which specifies a set of restrictions (called covenants) that protect the rights of the bondholders

Covenants:

Sinking fund: the firm agrees to periodically repurchase some proportion of the outstanding bonds prior to maturity- help ensure that the payment of the par value does not create a cash flow crisis

Subordination clauses: restrict the amount of additional borrowing- additional debt must be subordinated to existing debt: senior bondholders will be paid first in the event of bankruptcy


Júlio Lobão

105


Dividend restrictions: limit the dividends firms may pay- forces the firm to retain assets rather than pay them out to stockholders

Collateral: a specific asset pledged against possible default- if the collateral is property, the bond is called a mortgage bond- if the collateral takes the form of other securities held by the firm, the bond is called a collateral trust bond


Júlio Lobão

106


The Yield to Maturity and Default Risk

As the bond becomes more subject to default risk its price will fall and therefore its promised yield to maturity will rise


Júlio Lobão

107


Credit Default Swap (CDS): an insurance policy on the default of a bond- was designed to allow lenders to buy protection against losses on loans- the seller of the CDS will compensate the buyer in the event of a loan default or other credit event- the buyer of the CDS makes a series of payments to the seller and, in exchange, receives a payoff if the loan defaults


Júlio Lobão

108


G. The yield curve

Yield curve: a graph of the yields to maturity as a function of terms to maturity across bonds- also called the term structure of interest rates- rising yield curves are most commonly observed- interest rate risk vs. financing costs


Júlio Lobão

109


Yield curve theories

1) The expectations theory- yields to maturity are determined solely by expectations of future short-term interest rates- the slope of the yield curve is attributable to expectations ofchanges in short-term rates- relatively high (low) yields on long-term bonds reflect expectations of future increases (decreases) in short-term rates

Example:


Returns to twotwo-year

investmentstrategies

Júlio Lobão

110


- forward rate: the inferred short-term rate of interest for a future period that makes the expected total return of a long-term bond equal to that of rolling over short-term bonds

Example:

- two-year maturity bonds offer yields to maturity of 6%- three-year bonds have yields of 7%

- the forward rate for the third year will be 9.02%


( ) ( ) ( )323 1%61%71 f++=+

%02.93 =f

( ) ( ) ( )nn

nn

n fyy ++=+ −− 111 11

Júlio Lobão

111


2) The liquidity preference theory- shorter term bonds have more “liquidity” than longer term bonds, in the sense they offer greater price certainty- investors demand a risk premium on long-term bonds because these bonds are subject to greater interest rate risk than short-term bonds- the yield curve will be upward-sloping even in the absence of any expectation of future increases in interest rates- liquidity premium: the extra expected return demanded by investors as compensation for the greater risk of longer term bonds- the liquidity premium is measured by the spread between the forward rate of interest and the expected short rate

- issuers of bonds may also be willing to pay high yields on long-term bonds because it allows them to lock in an interest rate


( )nn rEfpremiumLiquidity −=

Júlio Lobão

112


3) The preferred habitat theory

Different bond investors prefer one maturity length over another- bond investors care about both maturity and return- they are only willing to buy bonds outside of their maturity preference if a risk premium for the maturity range is available


Júlio Lobão

113


A synthesis

The combination of varying expectations, liquidity premiums and maturity preferences can result in a wide array of yield-curve profiles- an upward-sloping curve does not in and of itself imply expectations of higher future interest rates because slope can result either from expectations, from risk premiums or from maturity preferences


Júlio Lobão

114


H. Interest rate risk

Interest rate sensitivity

1. bond prices and yields are inversely related: as yields increase (fall), bond prices fall (increase)

2. an increase in a bond’s yield to maturity results in a smaller price change than a decrease in yield of equal magnitude


A

BC

D

Júlio Lobão

115


3. prices of long-term bond tend to be more sensitive to interest rate changes than prices of short-term bonds

4. the sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases, i.e., interest rate risk is less than proportional to bond maturity- while bond B has six times the maturity of bond A, it has less than six times its interest rate sensitivity


A

BC

D

Júlio Lobão

116


5. interest rate risk is inversely related to the bond’s coupon rate, i.e., prices of low-coupon bonds are more sensitive to changes in interest rates than prices of high-coupon bonds- bond B has a higher coupon than that of bond C and is less sensitive to changes in yields

6. the sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling- bond C has a higher yield to maturity than bond D and is less sensitive to changes in yields


A

BC

D

Júlio Lobão

117


Duration

Macaulay’s duration: a measure of the effective maturity of a bond, defined as the weighted average of the times to each coupon or principal, with weights proportional to the present value of the payment

y: bond’s yield to maturity


( )price Bond

yCFwt

tt

+=

1/

∑=

=T

ttwtD

1

.

Júlio Lobão

118



Júlio Lobão

119


Duration is a measure of the interest rate sensitivity of a bond portfolio- when the interest rate varies, the percentage change in a bond’s price is proportional to its duration

- bond price volatility is proportional to the bond’s duration

Practitioners use the modified duration defined as :

- the percentage change in bond price is just the product of modified duration and the change in the bond’s yield to maturity


( )⎥⎦

⎤⎢⎣

⎡++Δ

−=Δ

yyD

PP

11.

yDD+

=1

*

yDPP

Δ−=Δ *

Júlio Lobão

120


Example:

A bond with maturity of 30 years has a coupon of 8% (paid annually) and a yield to maturity of 9%. Its price is 897.26€ and its duration is 11.37 years.What will happen to the bond price if the bond’s yield to maturity increases to 9.1%?


PyDP ..* Δ−=Δ

€36.9€26.897*001.0.09.137.11

−=−=ΔP

Júlio Lobão

121


Stock Market

Characteristics:

- it is the most popular market- it is one of the capital markets, i.e., where takes places the trading of long-term securities (maturities over one year)- from the perspective of the issuers, it is used to obtain long-term financing- from the perspective of the investors, it is used to make long-term investments (savings)- the main market participants are households, treasuries and firms- common stocks represent ownership shares in a corporation (capital owned by the corporation itself)

- stocks vs. bonds: voting rights, maturity, seniority

2. Financial Investments2.3. Stocks

Júlio Lobão

122


Common stock vs. preferred stock


Common Stock Preferred Stock

Ownership Own a portion of the firm Own a portion of the firm

Voting rights Can vote on company matters No voting rights usually

Pre-emptive rights

Grant rights on buying new shares when company issues new stock (to keep percentage of company they own the same)

Do not have pre-emptive rights

Return on capital (dividends)

Not guaranteed and paid only when company has excess profits. Never paid before preferred dividends

Guaranteed: fixed dividend per share that is set down in advance of purchase. Paid before any distributions to common stock holders

Asset claimsLast in line for claiming assets in the event of bankruptcy

Paid after debtors but before common stockholders if company goes bankrupt

Júlio Lobão

123


Valuing stocks

To compute the value of a stock is a very difficult task

Unlike most goods and services distributed by the economy, stocks have no direct intrinsic value- they are only instruments representing other, possible valuable, rights- those rights suffer from uncertainty

There are several asset pricing models which creates a indeterminacy problem:

«After decades of empirical research, the evidence is generally inconsistent with those models that make reasonably sharp predictions about asset return behavior, leaving financial economists with neither good models of prices nor accepted models of return behavior» (Brav and Heaton, 2003, p. 526)

«(…) there is no accepted theory by which to understand the worth of stocks and no clearly predictable consequences to changing one’s investments» (Shiller, 1984, p. 464).


Júlio Lobão

124


Valuing stocks

A. Valuation methods based on the balance sheet

1) Book-value per share

It only takes into account the past of the corporation (Equity).

2) Fair market value- estimate of the corporation market value (including assets and liabilities) based on a what a knowledgeable, willing and unpressured buyer would probably pay to a knowledgeable, willing and unpressured seller in the market.

If the value is higher than the shares market price, there are incentives for the acquisition of the corporation.

SharesgOutstandin TotalEquity Preferred -Equity er ShareholdTotal shareper value-Book =


Júlio Lobão

125


Valuing stocks

B. Valuation methods based on discounted cash flows

Asset’s value- sum of the present value of the expected future cash flows it will generate

The rate used to discount future cash flows reflects:- investors temporal preferences- capital productivity- inflation- uncertainty

When we want to estimate the value of stocks, the cash flow to consider is the dividend.- But what if the corporation does not pay any dividends?


Júlio Lobão

126


The retained earnings will likely generate higher dividends in the future- pay the debts- invest in financial or real assets (e.g., acquire other corporations)- share repurchase- capital budgeting (resource allocation)

1) Dividend discount model

1a) A special case: the Gordon-Shapiro model

( )∑∞

= +=

10 1t

tt

rDP

grDP−

= 10


Júlio Lobão

127


Dividend discount model: the Gordon-Shapiro model

Over the long run, no company can grow faster than the economy

Source: Burham (2005)

Example: Microsoft’s growth rate has slowed toward that of the US economy


Júlio Lobão

128



Assumptions:– Constant dividend nominal growth rate– Constant required return rate– Dividends growth rate is lower than the required return rate– Long-term analysis

Questions:– Estimate of the long-term dividend growth rate– Estimate of the required return rate– Effect of the business cycles on the variables of the model– Effect of the inflation on the variables of the model– Relation between the price and the dividend yield and growth


Júlio Lobão

129


We can rearrange the Gordon-Shapiro model

If a firm wants to increase its share value- should cut its dividend and invest more or- should cut investment and increase its dividends?

The answer will depend on the profitability of the firm’s investments- cutting the firm´s dividend to increase investment will raise the stock price if the new investments have a positive impact on the firm’s value


gPDr +=

0

1

=== Earnings

Investment New on Return*Investment New Earnings

Earnings in Change g

Earnings

Investment New on Return* Rate Retention* Earnings g ==

Investment New of Return* Rate Retention g =

Júlio Lobão

130



Limitations:- value that is very sensitive to the estimated rate of dividends growth

more suitable:- When we have a stable dividend payout- Firms/industries with stable growth

1b) A two stage dividend discount model with constant long-term growth:

∑=

= ++

+=

nt

tn

nt

t

rP

rDP

1 110 )1()1(

grDP n

n −= +

2

1


Júlio Lobão

131


Two stage dividend discount model

Limitations:- length of the abnormal growth period- abrupt transition from the first stage to the second stage

more suitable for situations in which the cash flows sources have the tendency to disappear:- Patents- abnormal returns caused by barriers to entry (e.g., economies of scale, legal barriers)

1c) H model:

( ) ( )n

n

n

na

grgD

grggHDP

−+

+−

−=

1** 000


Júlio Lobão

132


Forecasting dividends requires forecasting:- the firm’s earnings- dividend payout rate- future number of shares

But- future earnings depend on interest expenses

- interest rates depend on how much the firm borrows- the dividend payout rate and the future number of shares depend on whether the firm uses a portion of its earnings to repurchase shares

Borrowing and repurchase decisions are at management’s discretion- can be difficult to forecast reliably

There are two methods that allow us to avoid these difficulties.


Júlio Lobão

133


Valuing stocks

C. Total Payout and Free Cash Flow Valuation Models

An increasing number of firms have replaced dividend payouts with share repurchases.

This practice brings consequences to the dividend model:- the more cash the firm uses to repurchase shares, the less is available to pay dividends- by repurchasing shares, the firm decreases its share count

C1. Total payout model- ignores the firm’s choice between dividends and share repurchases- values all of the firm’s equity rather than a single share


Júlio Lobão

134


C1. Total payout model- values all of the firm’s equity rather than a single share

- to compute the share price we have to divide the value by the number of shares outstanding- discount the total payouts that the firm makes to shareholders

- dividends and share repurchases

C2. The Discounted Free Cash Flow Model- it is used to determine the total value of the firm to all investors- ignores the impact of the firm’s borrowing decisions on earnings- focuses on the cash flows to all the firm’s investors, both debt and equity holders


( )0gOutstandin Shares

sRepurchase and Dividends Total FuturePVP =0

( )Firm of Flow Cash Free FuturePVV Value Enterprise == 0

Júlio Lobão

135


Valuing stocks

D. Valuation methods based on market multiples

Price earnings ratio (PER)

There are other market multiples:- PBV = Price / Book Value per share- PCF = Price / Cash flow per share- PS = Price / Sales per share

(EPS) Shareper Earnings Shareper Value Market PER =

shareper earnings Expected* PERIndustry estimate price Stock =


Júlio Lobão

136


Problems when valuing stocks

1) Errors in estimating growth rates

- it is difficult to maintain high growth rates because of the increase in the competition

- the price is very sensitive to the growth estimate

2) Errors in estimating risk

- the variables of an equilibrium model have to be estimated- the CAPM has been empirically and theoretically challenged but the arbitrage

theory is not a valid alternative yet


Júlio Lobão

137


3) Errors in estimating dividends

- the dividend payout is difficult to estimate because it depends on the future investment opportunities and on the choices of the board of directors among other variables

- the changing expectations concerning the growth of the economy may make necessary to review the initial estimates

- the changes in prices in the short-term may result from the review of the estimates of the relevant variables

4) Limitations of multiples

- firms are not identical- does not take into account the important differences among firms- It does not help us to determine if an entire industry is overvalued

- ex. Internet boom of the late 1990s


Júlio Lobão

138


Equity risk premium

There are several concepts of equity risk premium:1) historical equity premium

- historical differential return of the stock market over treasuries2) expected risk premium

- expected differential return of the stock market over treasuries3) required risk premium

- incremental return of the market portfolio over the risk-free rate required by an investor in order to hold the market portfolio4) implied risk premium

- the required equity premium that arises from a pricing model and from assuming that the market price is correct

The historical equity premium has been extraordinary high: about 4% per year in real terms (Siegel, 2008).


Júlio Lobão

139


The observation of the historical equity risk premium suggests that:- the investors are risk-averse- the investors’ risk-aversion varies over time

- tends to be higher in times of greater uncertainty- when stock prices enter an extended phase of upward (downward) movement, the historical risk premium will climb (drop) to reflect past returns

- implied premiums will tend to move in the opposite direction since higher (lower) stock prices generally translate into lower (higher) returns

The equity premium risk with such high values as observed is one of the main puzzles in finance:- the investors would have to be extremely risk averse to justify annual risk premium of around 4% (some authors find values around 6% per year).


Júlio Lobão

140


The equity risk premium:- the historical equity premium has been very high in the last 200 years- averaged 1.4%, 3.4% and 5.9%, respectively, in each of the subperiods- in the all period it averaged 4% (= 6.8% - 2.8%) in real terms- the abnormally high equity premium since 1926 is not sustainable- with such very low real returns on bonds, firms financed their capital investments at a low cost which increased returns to shareholders

Source: Siegel (2008)


Júlio Lobão

141


The implied equity risk premium:- the implied equity risk premium computed from a bietapic asset pricing model- the equity premium understood as an indicator of risk aversion has remained positive and varying with time- the lower risk aversion coincided with the peak of the technology bubble in the end of 1999

Source: Damodaran (2009)

Source: Wikipedia


Júlio Lobão

142


The high value of the historical US equity premium does not result from a selection bias or a survivorship bias problem- despite the major disasters that affected many of these countries, such as war, hyperinflation, and depressions, all 16 countries offered substantially positive, after-inflation stock returns

- the US results are not a special case


Source: Siegel (2008)

Júlio Lobão

143


Possible explanations for the equity risk premium puzzle:

1) Selection bias- equity risk premium in the US is exceptionally high because it is an atypical economy, unusually successful- in fact, in other markets the equity premium risk tends to be lower but, as we have seen, is still too high to be justified only by the stock’s risk

2) Insurance against catastrophes- the observed risk of the shares in the past does not include the possibility of a very sharp drop in prices (“the catastrophe”)- an high equity premium risk reflects the possibility of such an event


Júlio Lobão

144



3) Tax reasons- the lowering of taxes on capital income could justify higher prices and, consequently, the high observed historical risk premiums- however, the observed variation on taxes is not sufficient to explain the puzzle

4) Preference for stable consumption and income- the share price tends to be procyclical:

- the market rises in times of higher economic growth and falls in times of recession when it is also more likely to fall the laborincome (unemployment)- if economic agents have a preference for stable income over time, they will require a higher risk premium for holding shares


Júlio Lobão

145



5) Myopic loss aversion- explanation from the field of behavioral finance- the investors are more sensitive to losses than to gains (loss aversion) and have difficulty in dealing with the consequences of long-term investments (financial myopia)- investors evaluate their portfolios over too short periods of time and become very sensitive to losses in these periods- therefore, they require a higher return for holding stocks than the ones predicted by the rational models to compensate them for these losses


Documents

Slides MFI Chap. 2