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第五章 債券與股票之評價

第五章 債券與股票之評價. 第四節 效率市場假說. 第一節 債券價值的計算. 第二節 股價模式. 第三節 股市行情導讀. Bonds and Their Valuation. Key features of bonds Bond valuation Measuring yield. Key Features of a Bond. 1. Par value: Face amount; paid at maturity. Assume $1,000.

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第五章 債券與股票之評價

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  1. 第五章 債券與股票之評價

  2. 第四節 效率市場假說 第一節 債券價值的計算 第二節 股價模式 第三節 股市行情導讀

  3. Bonds and Their Valuation • Key features of bonds • Bond valuation • Measuring yield

  4. Key Features of a Bond 1. Par value: Face amount; paid at maturity. Assume $1,000. 2. Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.

  5. 3. Maturity: Years until bond must be repaid. Declines. 4. Issue date: Date when bond was issued.

  6. 債券種類與契約限制 1. 債券種類 (1) 抵押債券(Mortgage Bonds) (2) 擔保債券(Guaranteed Bonds) (3) 信用債券(Debenture)： (4) 次級公司債(Subordinated Debenture) (5) 可收回債券(Callable Bonds) (6) 可賣回債券(Putable Bonds) (7) 收益公司債(Income Debenture)

  7. (8) 指數債券(Indexed Bonds) (9) 浮動利率債券(Floating-Rate Bonds) (10) 無息債券(Zero-Coupon Bonds) (11) 垃圾債券(Junk Bonds) (12) 抽獎債券(Lottery Bonds) (13) 實體資產債券(Physical Asset Bonds) (14) 可轉換公司債(Convertible Bonds, CBs) (15) 可交換公司債(Exchangeable Bonds, CBs) (16) 附認購權證公司債(Bonds with Warrants)

  8. How does adding a “call provision” affect a bond? • Issuer can refund if rates decline. That helps the issuer but hurts the investor. • Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds. • Most bonds have a deferred call and a declining call premium.

  9. What’s a sinking fund? • Provision to pay off a loan over its life rather than all at maturity. • Similar to amortization on a term loan. • Reduces risk to investor, shortens average maturity. • But not good for investors if rates decline after issuance.

  10. Sinking funds are generally handled in 2 ways 1. Call x% at par per year for sinking fund purposes. 2. Buy bonds on open market. Company would call if kd is below the coupon rate and bond sells at a premium. Use open market purchase if kd is above coupon rate and bond sells at a discount.

  11. 0 1 2 n Value CF1 CF2 CFn Financial Asset Values k ... CF CF CF 1 2 n + + + PV = . . . . ( ) ( ) ( ) 1 2 n k 1 + k 1 + 1 + k

  12. 第一節 債券價值的計算 • 一般債券支付固定利息，「到期日 (Maturity Date)」依「面額 (Par Value)」償還「本金 (Principal)」給債權人。 固定收益債券的收支 • 利息收入為 N期之「年金 (Annuity)」。

  13. (1) 每年付息之債券評價 「固定收益債券」的價格可利用下列公式計算： 其中 利息收入 INT = 票面利率 債券面額 = (ic‧F)， YTM為殖利率， N為目前至到期日之期數。

  14. (2) 半年付息之債券評價 半年付息一次債券的價格： • 當期收益率 (Current Yield) ：

  15. 例、債券價格之計算  期限：5 年 (7, 1998 ~ 6, 2003) ， 面額：100,000 元。 票面利率：8%，半年付息一次， 發行時殖利率 (YTM)：7%。 發行時的債券價格為何？  2000 年 7 月 1 日殖利率上升為 9%，債券價格為何？  2002 年 4 月 1 日殖利率下跌為 6%，債券價格為何？

  16. 1998 年 7 月 1 日發行時： 2000 年 7 月 1 日的價格：

  17. 2002 年 4 月 1 日時的價格：

  18. 利率與債券期間之關係 • 何者之價格受利率影響較大，長期或短期債券？ 到期日不同債券之價格變化 無論利率上升或下降，長期債券的價格變動較大。

  19. What’s interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk? Interest rate risk: Rising kd causes bond’s price to fall. kd 1-year Change 10-year Change 5% $1,048 $1,386 +4.8% -4.4% +38.6% -25.1% 10% 1,000 1,000 15% 956 749

  20. Value 10-year . 1,500 . . . . 1-year 1,000 . 500 kd 0 0% 5% 10% 15%

  21. What is reinvestment rate risk? The risk that CFs will have to be reinvested in the future at lower rates, reducing income. Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%.

  22. Year 1 income = $50,000. At year-end get back $500,000 to reinvest. If rates fall to 3%, income will drop from $50,000 to $15,000. Had you bought 30-year bonds, income would have remained constant.

  23. Long-term bonds: High interest rate risk, low reinvestment rate risk. • Short-term bonds: Low interest rate risk, high reinvestment rate risk. • Nothing is riskless!

  24. 債券重要觀念 • 「票面利率」「殖利率」 • 「票面利率」是約定的利率，為按期支付的固定比率。 • 「殖利率」因發行公司而異，並隨時間與總體環境變動。  債券價格與市場利率 • 市場利率  殖利率  已流通債券價格。 • 市場利率 殖利率  已流通債券價格。  債券價格不一定等於面額 • 債券價格 < 面額  折價債券 (Discount Bond)。 • 債券價格 < 面額  平價債券 (Par Bond)。 • 債券價格 > 面額  溢價債券 (Premium Bond)。

  25. Bond Yield Unlike the coupon interest rate, which is fixed, the bond’s yield varies from day to day depending on current market conditions. Moreover, the yield can be calculated in three different ways: 1.yield to maturity (YTM) 2.current yield 3.yield to call (YTC)

  26. What’s “yield to maturity”? • YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”

  27. What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? 0 1 9 10 kd=? ... 90 90 90 1,000 PV1 . . . PV10 PVM Find kd that “works”! 887

  28. Yield To Call If current interest rates are well below an outstanding bond’s coupon rate, then a callable bond is likely to be called, and investors will estimate its expected rate of return ass the yield to call(YTC) rather than as the YTM. if YTC=Kb PB=Σnt=1 I/(1+Kb)t + call price/(1+Kb)n

  29. 2. 零息債券價格的計算 「零息債券 (Zero Coupon Bond)」不附息票，從發行至到期日為止，不支付利息，以折現出售。  美國許多地方政府發行「零息債券」，而一些著名企業也在 1980 年代初開始發行「零息債券」。 「零息債券」的發行價格計算：

  30. 3. 債券之報價 債券之報價 票面利率 當期收益率 成交量 收盤價 價格變動

  31. Facts about Common Stock • Represents ownership. • Ownership implies control. • Stockholders elect directors. • Directors elect management. • Management’s goal: Maximize stock price.

  32. 第二節 股價模式 1. 股票的真值 公司支付股利之示意圖

  33. 如果每期的折現率相等，第 0 期的股票「真值」： 上式是將未來的股利收入折現的計算，折現後的「現值(PV)」即為「真值」，亦即理論股價 。

  34. 2. 特別股股價模式( zero growth stock) 利用下列方式簡化：

  35. 3. 戈登模式(constant growth stock) 公司股利固定成長率之示意圖

  36. (1) 戈登模式與股價報酬率 「戈登模式」可寫為： 股價報酬率： 若 k = r： 上式代表企業的成長率應該反應在股價上。

  37. (2) 戈登模式中成長率之估計 上式假設公司的「股東權益報酬率 (ROE)」不變，在保留盈餘後，會達到過去 ROE 的獲利水準。

  38. If we have supernormal growth of 30% for 3 years, then a long-run constant g = 10%, what is P0? k is still 12%. ^ • Can no longer use constant growth model. • However, growth becomes constant after 3 years.

  39. Nonconstant growth followed by constant growth: 0 1 2 3 4 ... ks=12% g = 30% g = 30% g = 30% g = 10% D0 = 0.25 0.3250 0.4225 0.5493 0.6042 0.2902 0.3368 0.3910 0 . 6042 $ P = = $30 . 21 21.5029 3 . 12 - 0 . 10 0 ^ 22.52 = P0

  40. 4. 隨機漫步模式 Pt = Pt-1 + et， 其中 Pt-1及 Pt分別為時間 t-1及時間 t的股價， et為時間 t的隨機誤差 「隨機漫步 (Random Walk)」代表無法準確預測股價。

  41. Preferred Stock • Hybrid security. • Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock. • However, unlike interest payments on bonds, companies can omit dividend payments on preferred stock without fear of pushing the firm into bankruptcy.

  42. What’s the expected return of preferred stock with Vp = $50 and annual dividend = $5?

  43. 第三節 股市行情導讀 1. 美國之股價報導 52 Weeks Yld Vol Net Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg 13711/16 89 IBM IBM 0.52 0.42 31 4338 12213/16 1191/2 1221/2 1/8 811/8 52 Merck MRK 1.36 1.85 27 2645 743/8 731/8 7315/165/16

  44. 補述 Charles Dow Edward Jones • 「道瓊工業指數 (Dow Jones Industrial Average,DJIA)」採用 30 家大型公司計算指數。 「道瓊工業指數 (DJIA)」的 30 家「藍籌股 (Blue Chips)」

  45. 2. 台灣之股價報導 • 台灣 2005 年 3 月前之檔次規定 台灣股價漲跌單位 (檔次) 之規定

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