Tuesday, August 17, 2010
CFA Level I - Reading 61
interest rates increase => bond price decreases
interest rates decrease=> bond price increases
coupon rate = yield => price = par
coupon rate > yield => price > par
coupon rate < yield => price < par
The longer the bond's maturity, the greater the bond's price sensitivity to changes in interest rates.
The lower the coupon rate, the greater the bond's price sensitivity to changes in interest rates.
The value of a bond with embedded options will change depending on how the value of the embedded options changes when interest rates change.
A decline in interest rates will result in an increase in the price of callable bond but not by as much as the price change of an otherwise comparable option-free bond.
Duration is a measure of the price sensitivity of a bond to a change in yield.
=(Price if yield decline - Price if yield rise) / (2 * Initial price * Change in yield in decimal)
Duration is approximately equal to the point in years where the investor receives half of the present value of the bond's cash flows.
Correct?:
The dollar change in price is approximately equal to the product of the duration and the current value of the bond divided by 100.
Incorrect:
If a bond has an effective duration of 7.5, it means that a 1% change in rates will result in a 7.5% change in price.
Because of convexity, it will be approximately a 7.5% change in price, not an actual 7.5% change in price.
Disadvantages of call division:
1. The cash flow pattern is not known with certainty.
2. The investor is exposed to reinvestment risk if the interest rates are lower.
3. The price appreciation potential will be reduced.
Call risk is composed of three components: the unpredictability of the cash flows, the compression of the bond’s price, and the high probability that when the bond is called the investor will be faced with less attractive investment opportunities.
Amortizing securities makes reinvestment risk greater.
Zero coupon bond may be attractive to certain investors because there is no reinvestment risk, but on the other hand, it exposes to greater interest rate risk.
Credit risk includes:
1. Default risk: the issuer will fail to satisfy the terms of the obligation.
2. Credit spread risk:
The yield on a bond is made up of 2 components: the yield on a similar risk-free bond and a premium above the yield on a default-free bond necessary to compensate for the risks associated with the bond. The risk premium is referred to as a yield spread.
The part of the risk premium or yield spread attributable to default risk is called the credit spread. If credit spread widen, the market price of the bond will decline.
The yield differential above the return on a benchmark security measures the credit spread risk. Credit spread risk is also known as the risk premium or spread.
3. Downgrade risk:
Triple A: prime grade
Double A: high quality grade
Single A: upper medium grade
Triple B: lower medium grade
Lower-rated: speculative grade
Investment grade bonds: AAA, AA, A, and BBB
Non-investment grade bonds ( speculative/high yield ): Below BBB
Liquidity Risk: the risk that the investor will have to sell a bond below its indicated value, where the indication is revealed by a recent transaction. The wider the bid-ask spread, the greater the liquidity risk.
Price of callable bond = price of option-free bond - price of embedded call option
Price of putable bond = price of option-free bond + price of embedded put option
If expected yield volatility increases, the price of the embedded call, or put, option will increase.
Price compression reduces the potential for price appreciation.
When a bond has a call provision, the potential for price appreciation is reduced, because the call caps the price of the bond near the call price, even if interest rates fall considerably. It is unlikely that investors would pay a price that exceeds the call price.
All else equal, reinvestment risk and price risk move in opposite directions. For example, when interest rates rise, bond prices decrease, but the loss is at least partially offset by decreased reinvestment risk (it is less likely that a bond will be called and bondholders can invest coupon payments at higher yields). When interest rates fall, price risk decreases because the bond value is rising and reinvestment risk increases because it is more likely that the issuer/borrower will call the security and the bondholder must reinvest coupon payments at lower yields.
Technical default usually refers to an issuer’s violation of bond covenants, such as debt ratios, rather than the failure to pay interest or principal.
Sovereign risk: the risk that as a result of actions of the foreign government, there may be either a default or an adverse price change even in the absence of a default.
1. Unwillingness of a foreign gov't to pay.
2. The inability to pay due to unfavorable economic conditions in the country.
interest rates decrease=> bond price increases
coupon rate = yield => price = par
coupon rate > yield => price > par
coupon rate < yield => price < par
The longer the bond's maturity, the greater the bond's price sensitivity to changes in interest rates.
The lower the coupon rate, the greater the bond's price sensitivity to changes in interest rates.
The value of a bond with embedded options will change depending on how the value of the embedded options changes when interest rates change.
A decline in interest rates will result in an increase in the price of callable bond but not by as much as the price change of an otherwise comparable option-free bond.
Duration is a measure of the price sensitivity of a bond to a change in yield.
=(Price if yield decline - Price if yield rise) / (2 * Initial price * Change in yield in decimal)
Duration is approximately equal to the point in years where the investor receives half of the present value of the bond's cash flows.
Correct?:
The dollar change in price is approximately equal to the product of the duration and the current value of the bond divided by 100.
Incorrect:
If a bond has an effective duration of 7.5, it means that a 1% change in rates will result in a 7.5% change in price.
Because of convexity, it will be approximately a 7.5% change in price, not an actual 7.5% change in price.
Disadvantages of call division:
1. The cash flow pattern is not known with certainty.
2. The investor is exposed to reinvestment risk if the interest rates are lower.
3. The price appreciation potential will be reduced.
Call risk is composed of three components: the unpredictability of the cash flows, the compression of the bond’s price, and the high probability that when the bond is called the investor will be faced with less attractive investment opportunities.
Amortizing securities makes reinvestment risk greater.
Zero coupon bond may be attractive to certain investors because there is no reinvestment risk, but on the other hand, it exposes to greater interest rate risk.
Credit risk includes:
1. Default risk: the issuer will fail to satisfy the terms of the obligation.
2. Credit spread risk:
The yield on a bond is made up of 2 components: the yield on a similar risk-free bond and a premium above the yield on a default-free bond necessary to compensate for the risks associated with the bond. The risk premium is referred to as a yield spread.
The part of the risk premium or yield spread attributable to default risk is called the credit spread. If credit spread widen, the market price of the bond will decline.
The yield differential above the return on a benchmark security measures the credit spread risk. Credit spread risk is also known as the risk premium or spread.
3. Downgrade risk:
Triple A: prime grade
Double A: high quality grade
Single A: upper medium grade
Triple B: lower medium grade
Lower-rated: speculative grade
Investment grade bonds: AAA, AA, A, and BBB
Non-investment grade bonds ( speculative/high yield ): Below BBB
Liquidity Risk: the risk that the investor will have to sell a bond below its indicated value, where the indication is revealed by a recent transaction. The wider the bid-ask spread, the greater the liquidity risk.
Price of callable bond = price of option-free bond - price of embedded call option
Price of putable bond = price of option-free bond + price of embedded put option
If expected yield volatility increases, the price of the embedded call, or put, option will increase.
Price compression reduces the potential for price appreciation.
When a bond has a call provision, the potential for price appreciation is reduced, because the call caps the price of the bond near the call price, even if interest rates fall considerably. It is unlikely that investors would pay a price that exceeds the call price.
All else equal, reinvestment risk and price risk move in opposite directions. For example, when interest rates rise, bond prices decrease, but the loss is at least partially offset by decreased reinvestment risk (it is less likely that a bond will be called and bondholders can invest coupon payments at higher yields). When interest rates fall, price risk decreases because the bond value is rising and reinvestment risk increases because it is more likely that the issuer/borrower will call the security and the bondholder must reinvest coupon payments at lower yields.
Technical default usually refers to an issuer’s violation of bond covenants, such as debt ratios, rather than the failure to pay interest or principal.
Sovereign risk: the risk that as a result of actions of the foreign government, there may be either a default or an adverse price change even in the absence of a default.
1. Unwillingness of a foreign gov't to pay.
2. The inability to pay due to unfavorable economic conditions in the country.
Friday, August 13, 2010
CFA Level I - Reading 60
The affirmative covenants of indenture set forth activities that the borrower promises to do. The negative covenants set forth certain limitations and restrictions on the borrower's activities.
Step-Up Notes: The securities whose coupon rate increases over time.
Single step-up notes: There is only one change (or step-up).
Multiple step-up notes: There is more than one changes.
Deferred Coupon Bonds
Accrual bonds, unlike zero-coupon bonds, do not always sell at a discount to face value. The interest accrues forward and thus the bonds are likely to sell for more than face value.
Floating-Rate Securities: Coupon rate = Reference rate + Quoted margin
A floater could have a Cap, the maximum coupon rate that will be paid, or a Floor, the minimum coupon rate.
Inverse floaters: whose coupon rate move in the opposite direction from the change in the reference rate.
Coupon = K - L * (Reference Rate)
Full Price (or Dirty Price) = bond price + accrued interest
A bond in which the buyer must pay the seller accrued interest is said to be trading cum-coupon (with coupon).
If the buyer forgoes the next coupon payment, the bond is said to be trading ex-coupon (without coupon).
In the instance that the bond issuer defaulted the interest payments, and the bond is sold without accrued interest, it is called to be traded flat.
If the issuer is not required to make any principle repayment prior to the maturity date, such bonds are said to have a bullet maturity. Otherwise the bonds are said to be amortizing securities, for example, mortgage-back securities, or sinking funds.
Callable bonds:
If the bond issuer may not call the bond for a number of years, the issue is said to have a deferred call. The date at which the bond may first be called is referred to as the first call date.
When less than entire issue is called, the certificates to be called are either selected randomly or on a pro rata basis. Pro rata redemption means that all bondholders will have the same percentage of their holdings redeemed.
A make-whole premium provision (or a yield-maintenance premium provision) provides a formula for determining the premium that an issuer must pay to call an issue.
Call protection is much more robust than refunding protection.
Sinking fund provision: An indenture may require the issuer to retire a specified portion of the issue each year.
Convertible bond is an issue that grants the bondholder the right to convert the bond for a specified number of shares of common stock.
Put provision grants the bondholder the right to sell the issue back to the issuer at a specified price on designated dates.
A nondollar-denominated issue is one in which payments are not denominated in US dollar.
Regular redemption price refers to bonds being called according to the provisions specified in the bond indenture. When bonds are redeemed to comply with a sinking fund provision or because of a property sale mandated by government authority, the redemption prices (typically par value) are referred to as "special redemption prices." There is no such thing as a specific redemption price.
Refunding from a new debt issue at a higher interest rate is not prohibited, however their purchase cannot be funded by the simultaneous issuance of lower coupon bonds.
Step-Up Notes: The securities whose coupon rate increases over time.
Single step-up notes: There is only one change (or step-up).
Multiple step-up notes: There is more than one changes.
Deferred Coupon Bonds
Accrual bonds, unlike zero-coupon bonds, do not always sell at a discount to face value. The interest accrues forward and thus the bonds are likely to sell for more than face value.
Floating-Rate Securities: Coupon rate = Reference rate + Quoted margin
A floater could have a Cap, the maximum coupon rate that will be paid, or a Floor, the minimum coupon rate.
Inverse floaters: whose coupon rate move in the opposite direction from the change in the reference rate.
Coupon = K - L * (Reference Rate)
Full Price (or Dirty Price) = bond price + accrued interest
A bond in which the buyer must pay the seller accrued interest is said to be trading cum-coupon (with coupon).
If the buyer forgoes the next coupon payment, the bond is said to be trading ex-coupon (without coupon).
In the instance that the bond issuer defaulted the interest payments, and the bond is sold without accrued interest, it is called to be traded flat.
If the issuer is not required to make any principle repayment prior to the maturity date, such bonds are said to have a bullet maturity. Otherwise the bonds are said to be amortizing securities, for example, mortgage-back securities, or sinking funds.
Callable bonds:
If the bond issuer may not call the bond for a number of years, the issue is said to have a deferred call. The date at which the bond may first be called is referred to as the first call date.
When less than entire issue is called, the certificates to be called are either selected randomly or on a pro rata basis. Pro rata redemption means that all bondholders will have the same percentage of their holdings redeemed.
A make-whole premium provision (or a yield-maintenance premium provision) provides a formula for determining the premium that an issuer must pay to call an issue.
Call protection is much more robust than refunding protection.
Sinking fund provision: An indenture may require the issuer to retire a specified portion of the issue each year.
Convertible bond is an issue that grants the bondholder the right to convert the bond for a specified number of shares of common stock.
Put provision grants the bondholder the right to sell the issue back to the issuer at a specified price on designated dates.
A nondollar-denominated issue is one in which payments are not denominated in US dollar.
Regular redemption price refers to bonds being called according to the provisions specified in the bond indenture. When bonds are redeemed to comply with a sinking fund provision or because of a property sale mandated by government authority, the redemption prices (typically par value) are referred to as "special redemption prices." There is no such thing as a specific redemption price.
Refunding from a new debt issue at a higher interest rate is not prohibited, however their purchase cannot be funded by the simultaneous issuance of lower coupon bonds.
Wednesday, August 11, 2010
CFA Level I - Reading 59
Trailing P/E (sometimes referred to as Current P/E) is a stock's current market price divided by the most recent four quarters' EPS. In such calculations, EPS is sometimes referred to as trailing 12 months (TTM) EPS. Trailing P/E is the one published in financial newspapers' stock listings.
Leading P/E (also called the forward P/E, or prospective P/E) is a stock's current price divided by next year's expected earnings.
For companies with rising earnings, the leading P/E will be smaller than the trailing P/E.
When calculating trailing P/E, an analyst must consider the following:
1. transitory, nonrecurring components of earnings that are company specific;
2. transitory components of earnings due to cyclicality (business or industry cyclicality);
3. differences in accounting methods;
4. potential dilution of EPS.
Nonrecurring items (such as gains and losses form the sale of assets, asset writedowns, provisions for future losses, and change in accounting estimates) often appear in the income from continuing operations portion of the Income Statement. An analyst should pay particular attention to the Income Statement, its footnotes, and management discussion and analysis.
Two of several methods to calculate Business-cycle-adjusted EPS:
1. historical average EPS: the average EPS over the most recent full cycle. However, this method doesn't account for changes in the company's size.
2. average return on equity: the average return on equity (ROE) from the most recent full cycle, multiplied by current book value per share. This method reflects more accurately the effect on EPS of growth or shrinkage in the company's size.
Basic earnings per share reflects total earnings divided by the weighted-average number of shares actually outstanding during the period.
Diluted earnings per share is the division by the number of shares that would be outstanding if holders of securities such as executive stock options, equity warrants, and convertible bonds exercised their options.
Among the positive P/Es, the stock with the lowest P/E has the lowest purchase cost per currency unit of earnings. In order to include negative P/Es in the ranking, we could use earnings yield ratio (E/P).
Price to Book Value
Rationales for using P/BV:
1. Book value is a cumulative balance sheet amount, book value is generally positive even when EPS is negative.
2. Book value per share is more stable than EPS, P/BV maybe more meaningful than P/E when EPS is abnormally high or low, or is highly variable.
3. Book value per share has been viewed as more appropriate for valuing companies composed chiefly of liquid assets, such as finance, investment, insurance, and banking institutions.
4. Book value has also been used in valuation of companies that are not expected to continue as a going concern.
5. Differences in P/BVs may be related to differences in long-term average returns.
Possible drawbacks of P/BVs:
1. Other assets besides those recognized in accounting may be critical operating factors, such as human capital.
2. P/B can be misleading as a valuation indicator when significant differences exist among companies examined in terms of the level of assets used. Such differences may reflect differences in business models.
3. Accounting effects on book value may compromise book value as a measure of shareholders' investment in the company.
4. In the accounting of most countries, including the US, book value largely reflects the historical purchase costs of assets, as well as accumulated accounting depreciation expense. Inflation as well as technological change eventually drive a wedge between the book value and the market value of assets. As a result, book value per share often poorly reflects the value of shareholders' investments.
Calculation:
common shareholders' equity = shareholders' equity - total value of equity claims that are senior to common stock
book value per share = common shareholders' equity / # of common shares outstanding
Calculating tangible book value per share involves subtracting intangible assets from common shareholders' equity. It is not so appropriate to separate patents, but might be appropriate to subtract goodwill.
P/S:
Rationales for using P/S:
1. Sales are generally less subject to distortion or manipulation.
2. Sales are positive even when EPS is negative.
3. Sales are generally more stable than EPS. P/S may be more meaningful than P/E when EPS is abnormally high/low.
4. P/S has been viewed as appropriate for valuing the stock of mature, cyclical, and zero-income companies.
5. Differences in P/S may be related to differences in long-term average returns.
Drawbacks:
1. A business may show high growth in sales even when it is not operating profitably.
2. P/S doesn't reflect a company's expenses, differences in P/S may be explained by differences in cost structure.
3. Revenue recognition practices offer the potential to distort P/S.
Bill-and-Hold involves selling products but not delivering those products until a later date.
P/CF:
Rationales for using P/CF:
1. Cash Flow is less subject to manipulation than earnings.
2. Cash flow is generally more stable than earnings.
3. Using P/CF rather than P/E address the issue of differences in accounting conservatism between companies (differences in the quality of earnings).
4. Differences in P/CF may be related to differences in long-term average returns.
Drawbacks:
1. When the EPS plus noncash charges approximation to cash flow from operations is used, items affecting actual cash flow from operations, such as noncash revenue and net changes in working capital, are ignored.
2. Theory views free cash flow to equity rather than cash flow as the appropriate variable for valuation. FCFE does have the possible drawback of being more volatile.
Leading P/E (also called the forward P/E, or prospective P/E) is a stock's current price divided by next year's expected earnings.
For companies with rising earnings, the leading P/E will be smaller than the trailing P/E.
When calculating trailing P/E, an analyst must consider the following:
1. transitory, nonrecurring components of earnings that are company specific;
2. transitory components of earnings due to cyclicality (business or industry cyclicality);
3. differences in accounting methods;
4. potential dilution of EPS.
Nonrecurring items (such as gains and losses form the sale of assets, asset writedowns, provisions for future losses, and change in accounting estimates) often appear in the income from continuing operations portion of the Income Statement. An analyst should pay particular attention to the Income Statement, its footnotes, and management discussion and analysis.
Two of several methods to calculate Business-cycle-adjusted EPS:
1. historical average EPS: the average EPS over the most recent full cycle. However, this method doesn't account for changes in the company's size.
2. average return on equity: the average return on equity (ROE) from the most recent full cycle, multiplied by current book value per share. This method reflects more accurately the effect on EPS of growth or shrinkage in the company's size.
Basic earnings per share reflects total earnings divided by the weighted-average number of shares actually outstanding during the period.
Diluted earnings per share is the division by the number of shares that would be outstanding if holders of securities such as executive stock options, equity warrants, and convertible bonds exercised their options.
Among the positive P/Es, the stock with the lowest P/E has the lowest purchase cost per currency unit of earnings. In order to include negative P/Es in the ranking, we could use earnings yield ratio (E/P).
Price to Book Value
Rationales for using P/BV:
1. Book value is a cumulative balance sheet amount, book value is generally positive even when EPS is negative.
2. Book value per share is more stable than EPS, P/BV maybe more meaningful than P/E when EPS is abnormally high or low, or is highly variable.
3. Book value per share has been viewed as more appropriate for valuing companies composed chiefly of liquid assets, such as finance, investment, insurance, and banking institutions.
4. Book value has also been used in valuation of companies that are not expected to continue as a going concern.
5. Differences in P/BVs may be related to differences in long-term average returns.
Possible drawbacks of P/BVs:
1. Other assets besides those recognized in accounting may be critical operating factors, such as human capital.
2. P/B can be misleading as a valuation indicator when significant differences exist among companies examined in terms of the level of assets used. Such differences may reflect differences in business models.
3. Accounting effects on book value may compromise book value as a measure of shareholders' investment in the company.
4. In the accounting of most countries, including the US, book value largely reflects the historical purchase costs of assets, as well as accumulated accounting depreciation expense. Inflation as well as technological change eventually drive a wedge between the book value and the market value of assets. As a result, book value per share often poorly reflects the value of shareholders' investments.
Calculation:
common shareholders' equity = shareholders' equity - total value of equity claims that are senior to common stock
book value per share = common shareholders' equity / # of common shares outstanding
Example:
Given the following information, compute price/book value.
- Book value of assets = $550,000
- Total sales = $200,000
- Net income = $20,000
- Dividend payout ratio = 30%
- Operating cash flow = $40,000
- Price per share = $100
- Shares outstanding = 1000
- Book value of liabilities = $500,000
Book value of equity = $550,000 - $500,000 = $50,000 Market value of equity = ($100)(1000) = $100,000
Price/Book = $100,000/$50,000 = 2.0X
Price/Book = $100,000/$50,000 = 2.0X
Calculating tangible book value per share involves subtracting intangible assets from common shareholders' equity. It is not so appropriate to separate patents, but might be appropriate to subtract goodwill.
P/S:
Rationales for using P/S:
1. Sales are generally less subject to distortion or manipulation.
2. Sales are positive even when EPS is negative.
3. Sales are generally more stable than EPS. P/S may be more meaningful than P/E when EPS is abnormally high/low.
4. P/S has been viewed as appropriate for valuing the stock of mature, cyclical, and zero-income companies.
5. Differences in P/S may be related to differences in long-term average returns.
Drawbacks:
1. A business may show high growth in sales even when it is not operating profitably.
2. P/S doesn't reflect a company's expenses, differences in P/S may be explained by differences in cost structure.
3. Revenue recognition practices offer the potential to distort P/S.
Bill-and-Hold involves selling products but not delivering those products until a later date.
P/CF:
Rationales for using P/CF:
1. Cash Flow is less subject to manipulation than earnings.
2. Cash flow is generally more stable than earnings.
3. Using P/CF rather than P/E address the issue of differences in accounting conservatism between companies (differences in the quality of earnings).
4. Differences in P/CF may be related to differences in long-term average returns.
Drawbacks:
1. When the EPS plus noncash charges approximation to cash flow from operations is used, items affecting actual cash flow from operations, such as noncash revenue and net changes in working capital, are ignored.
2. Theory views free cash flow to equity rather than cash flow as the appropriate variable for valuation. FCFE does have the possible drawback of being more volatile.
Tuesday, August 10, 2010
CFA Level I - Reading 57 & 58
An analyst should take into account how broad structural changes will affect specific industries over time. Four types of structural changes are:
A firm’s earnings per share (EPS) can be estimated using the following equation:
- Demographics: Demographic factors include age distribution and population changes, as well as changes in income distribution, ethnic composition of the population, and trends in the geographical distribution of the population. As a large segment of the population reaches their twenties, residential construction, furniture, and related industries will see increased demand. An aging of the overall population can mean significant growth for the healthcare industry and developers of retirement communities.
- Lifestyles: An example of the effect of changing lifestyles on industry growth prospects is the increase in meals consumed outside the home and catalog sales, as the percentage of families with two employed spouses has increased. Consumption patterns are also affected by current perceptions of what is "in style" and trends in consumer tastes in recreation, entertainment, and other areas of discretionary expenditure.
- Technology: Changes in technology have had very important consequences for many industries over time. Change in the technology of transportation and communications have certainly had important effects on these industries, both in terms of products and services consumed but also in their production and pricing. Technological advances in computers and microprocessors in general have lead to sweeping changes in how inventory is managed and how products are distributed in many industries, particularly in the retailing industry.
- Politics and regulation: Changes in the political climate and changes in specific government regulations can also have significant effects on particular industries. The imposition of tariffs on steel will lead to increased domestic production and profitability; the rise of terrorist activity has helped some industries and imposed costs on others such as the airline and shipping industries; and requirements of a minimum wage and the widespread expectation of employment benefits packages have affected hiring practices and production methods, especially in labor intensive industries. Regulation of the introduction and sale of everything from new drugs to genetically engineered crops has important implications for many industries as well.
A firm’s earnings per share (EPS) can be estimated using the following equation:
Expected EPS = [(sales)(EBITDA %) – depreciation – interest](1 – tax rate)A firm’s expected earnings multiplier (P/E) can be calculated using either of two methods:
- Macroanalysis approach estimates the company’s P/E ratio by comparing it to industry and market P/E ratios.
- Microanalysis approach calculates a point estimate of the firm’s expected P/E ratio.
One way to evaluate the purchase of a stock is to compare the intrinsic value (based on the present value of expected dividends or cash flows) to the current market price. An alternative is to assume that the market price will move to the intrinsic value over some period and then compare the expected total return over the period to the investor’s required rate of return.
Estimate the firm’s projected dividend payout ratio, D1/E1. This is done with comparative analysis of the firm’s payout history, stated goals, and industry.
Estimate the firm’s required rate of return on equity: k = RFR + [E(RMKT – RFR)]Beta
Estimate the firm’s expected growth rate: g = (retention rate)(ROE)
Compute the firm’s future earnings multiplier: (P/E)1 = (D1/E1) / (k – g)
Sunday, August 8, 2010
Duration
Duration is a measure of the sensitivity of the price of a bond to the change of interest rate. It's widely used as a risk measure for bonds. The higher a bond's duration, the more risky it is.
Excel provides a formula to calculate Duration (also refers to Macauley Duration) and MDuration (somewhat inaccurately termed by Excel as Macauley Duration), using the same syntax:
Duration(settlement, maturity, coupon, yield, frequency, basis)
MDuration(settlement, maturity, coupon, yield, frequency, basis)
The MDuration can be used to calculate the volatility of a bond. The difference between Duration and MDuration is as follow:
MDuration = Duration / [ 1 + (yield / number of coupon payment per year) ]
The effects of maturity and coupon on duration are showed as follow:
* Download the Excel file - Duration, Effects of Maturity and Coupon *
Excel provides a formula to calculate Duration (also refers to Macauley Duration) and MDuration (somewhat inaccurately termed by Excel as Macauley Duration), using the same syntax:
Duration(settlement, maturity, coupon, yield, frequency, basis)
MDuration(settlement, maturity, coupon, yield, frequency, basis)
The MDuration can be used to calculate the volatility of a bond. The difference between Duration and MDuration is as follow:
MDuration = Duration / [ 1 + (yield / number of coupon payment per year) ]
The effects of maturity and coupon on duration are showed as follow:
Saturday, August 7, 2010
CFA Level I - Reading 56
There are 2 valuation approaches. The difference between these 2 approaches is the perceived importance of the economy and a firm's industry on the valuation:
1. The top-down, three-step approach. The advocates of this approach believe that both the economy/market and the industry effect have a significant impact on the total returns for individual stocks.
1) Analysis of alternative economies and security markets.
2) Analysis of alternative industries.
3) Analysis of individual companies and stocks.
2. The bottom-up, stock valuation, stockpicking approach. Those who employ this approach contend that it is possible to find stock that are undervalued relative to their market price, and these stocks will provide superior returns regardless of the market and industry outlook.
Discount Dividend Model
Present Value of Operating Free Cash Flow
Present Value of Free Cash Flow to Equty
Relative Valuation Techniques:
Earning Multiplier Model (P/E ratio): Current Market Price / Expected Earnings
P=D1/(k-g) => P/E1 = (D1/E1) / (k-g)
The spread of k and g is the main determinant of the size of the P/E
1. The top-down, three-step approach. The advocates of this approach believe that both the economy/market and the industry effect have a significant impact on the total returns for individual stocks.
1) Analysis of alternative economies and security markets.
2) Analysis of alternative industries.
3) Analysis of individual companies and stocks.
2. The bottom-up, stock valuation, stockpicking approach. Those who employ this approach contend that it is possible to find stock that are undervalued relative to their market price, and these stocks will provide superior returns regardless of the market and industry outlook.
Discount Dividend Model
Present Value of Operating Free Cash Flow
Present Value of Free Cash Flow to Equty
Relative Valuation Techniques:
Earning Multiplier Model (P/E ratio): Current Market Price / Expected Earnings
P=D1/(k-g) => P/E1 = (D1/E1) / (k-g)
The spread of k and g is the main determinant of the size of the P/E
Friday, August 6, 2010
Bought BP Call Options
Today finally bought BP Jan21, 2012 Call Option, with strike $30. The rationale behind this purchase has threefold.
First, I tried to pick a call with a big Delta such that I could enjoy the largest exposure to the price change of the underlying. While Deep ITM Calls commonly have larger than 90 Deltas, the prices are also high, which doesn't fit my budget. The BP 120121C30 has a 80 Delta, which gives me a large enough exposure based on the budget I have.
Second, BP 120121C30 has 16 months to mature, which gives the Call a relatively long period to decay.
Third, BP 120121C30 has an open interest of 6630. It is much active, so as liquid, than other 2012Jan Calls.
First, I tried to pick a call with a big Delta such that I could enjoy the largest exposure to the price change of the underlying. While Deep ITM Calls commonly have larger than 90 Deltas, the prices are also high, which doesn't fit my budget. The BP 120121C30 has a 80 Delta, which gives me a large enough exposure based on the budget I have.
Second, BP 120121C30 has 16 months to mature, which gives the Call a relatively long period to decay.
Third, BP 120121C30 has an open interest of 6630. It is much active, so as liquid, than other 2012Jan Calls.
Option chain:
VBA for Variance-Covariance Matrix
Function VarCov(rng As Range) As Variant
Dim i As Integer
Dim j As Integer
Dim colnum As Integer
Dim matrix() As Double
colnum = rng.Columns.Count
ReDim matrix(colnum - 1, colnum - 1)
For i = 1 To colnum
For j = 1 To colnum
matrix(i - 1, j - 1) = Application.WorksheetFunction.Covar(rng.Columns(i), rng.Columns(j))
Next j
Next i
VarCov = matrix
End Function
Dim i As Integer
Dim j As Integer
Dim colnum As Integer
Dim matrix() As Double
colnum = rng.Columns.Count
ReDim matrix(colnum - 1, colnum - 1)
For i = 1 To colnum
For j = 1 To colnum
matrix(i - 1, j - 1) = Application.WorksheetFunction.Covar(rng.Columns(i), rng.Columns(j))
Next j
Next i
VarCov = matrix
End Function
Thursday, August 5, 2010
CFA Level I - Reading 55
A mispricing is any predictable deviation from a normal or expected return.
Wednesday, August 4, 2010
CFA Level I - Reading 54 Con't
Behavioral Finance
One major bias is the propensity of investors to hold on to "losers" too long and sell "winners" too soon.
Confirmation bias: growth companies' confidence in forecasts, which causes analysts to overestimate growth rates for growth companies ans overemphasize good news and ignore negative news.
When there is a shift in sentiment, noise traders (nonprofessional with no special information) move together, which increase the prices and the volatility of securities during trading hours.
Escalation bias: investors put more money into a failure that they feel responsible for rather into a success. This also refers to "averaging down" on an investment that has declined in value since the initial purchase rather than consider selling the stock if it was a mistake.
Fusion investing is the integration of 2 elements of investment valuation - fundamental value and investor sentiment. The market price of securities is its fundamental value plus a term that indicates the demand from noise traders who reflect investor sentiment.
Portfolio management with superior analysts: the superior analysts should be encouraged to concentrate their efforts in mid-cap and small-cap. The superior analysts should pay particular attention to the BV/MV, to the size of stocks being analyzed, and to the monetary policy environment.
If you lack access to superior analysts, you should:
1. Determine and qualify your risk preferences.
2. Construct the appropriate risk portfolio by dividing the total portfolio between risk-free assets and a risky assets.
3. Diversify completely on a global basis to eliminate all unsystematic risk.
4. Maintain the specified risk level by rebalancing when necessary.
5. Minimize total transaction costs.
One major bias is the propensity of investors to hold on to "losers" too long and sell "winners" too soon.
Confirmation bias: growth companies' confidence in forecasts, which causes analysts to overestimate growth rates for growth companies ans overemphasize good news and ignore negative news.
When there is a shift in sentiment, noise traders (nonprofessional with no special information) move together, which increase the prices and the volatility of securities during trading hours.
Escalation bias: investors put more money into a failure that they feel responsible for rather into a success. This also refers to "averaging down" on an investment that has declined in value since the initial purchase rather than consider selling the stock if it was a mistake.
Fusion investing is the integration of 2 elements of investment valuation - fundamental value and investor sentiment. The market price of securities is its fundamental value plus a term that indicates the demand from noise traders who reflect investor sentiment.
Portfolio management with superior analysts: the superior analysts should be encouraged to concentrate their efforts in mid-cap and small-cap. The superior analysts should pay particular attention to the BV/MV, to the size of stocks being analyzed, and to the monetary policy environment.
If you lack access to superior analysts, you should:
1. Determine and qualify your risk preferences.
2. Construct the appropriate risk portfolio by dividing the total portfolio between risk-free assets and a risky assets.
3. Diversify completely on a global basis to eliminate all unsystematic risk.
4. Maintain the specified risk level by rebalancing when necessary.
5. Minimize total transaction costs.
Tuesday, August 3, 2010
CFA Level I - Reading 54
Weak-form EMH: current stock prices fully reflect all security market information.
Semistrong-form EMH: security prices adjust rapidly to the release of all public information. The semistrong-form encompass the weak-form, and also includes all nonmarket information, such as earnings and dividend announcements, P/E, D/P, P/BV, stock splits, economy and political news, ect.
Strong-form EMH: stock prices fully reflect all information from the public and private sources.
When the two most significant variables - the dividend yield (D/P) and the bond default spread - are high, it implies that investors are expecting or requiring a high return on stocks and bonds. This occurs during poor economic environments.
Low P/E ratio stocks (low-growth firms) experienced superior risk-adjusted returns, whereas high P/E (high-growth firms) had significantly inferior risk-adjusted results.
Hypothesis of the inverse relation between the Price-Earnings/Growth Rate (PEG) ratio and the return: low PEG (<1) will have above-average returns, while high PEG (>3 or 4) will have below-average returns.
Small firms outperformed the large firms after considering risk and transaction costs, assuming annual rebalancing. Small firm effect is a long-term phenomenon.
A positive relationship between BV/MV ratio and the average return. More importantly, both Size and BV/MV ratio are significant when included together and they dominate other ratios. (It might only works during expansive monetary policy.)
Most studies found no short-term or long-term positive impact on security returns because of a stock split, although the results are not unanimous.
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