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金 融 市 场 学. 攀 登. 金融市场学. 债券. 时间价值. 货币是有时间价值的. 金融工具分类与时间价值. 简易贷款 年金 附息债券 贴现债券. 现值和终值. 简易贷款 年金 附息债券 贴现债券. 到期收益率. 简易贷款 年金 附息债券 贴现债券. 利率. 折算惯例 比例法 复利法 名义利率与实际利率 差别在于是否考虑了通货膨胀的影响 即期利率与远期利率 利率水平的决定 可贷资金模型 流动性偏好模型. 利率的结构. 预期假说 市场分割假说 偏好停留假说. 债券特征.
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金 融 市 场 学 攀 登
金融市场学 债券
时间价值 货币是有时间价值的
金融工具分类与时间价值 • 简易贷款 • 年金 • 附息债券 • 贴现债券
现值和终值 • 简易贷款 • 年金 • 附息债券 • 贴现债券
到期收益率 • 简易贷款 • 年金 • 附息债券 • 贴现债券
利率 • 折算惯例 • 比例法 • 复利法 • 名义利率与实际利率 • 差别在于是否考虑了通货膨胀的影响 • 即期利率与远期利率 • 利率水平的决定 • 可贷资金模型 • 流动性偏好模型
利率的结构 • 预期假说 • 市场分割假说 • 偏好停留假说
债券特征 • 面值(Face or par value) • 息票率(Coupon rate) • 零息票债券 • 利息支付方式 • 债券契约
各类债券 • 国债 • 企业债 • 地方政府债券 • 海外债 • 创新债券 • 指数化债券 • 浮动和反向债券
Money Markets • US Treasury Bills (T-Bills) • Certificates of Deposit (CD) • Commercial paper (CP) • Bankers’ acceptances • Eurodollars • Repos and Reverses • Federal Funds
US Treasury Bills • Initial maturities are • 91-182 days, offered weekly • 52 weeks, offered monthly • Competitive and noncompetitive (10-20%) bids. • The investor buys the instrument at discount • bid-ask (spread) represents the profit for the dealer • quotes use the bank discount yield. • Exempt of state and local taxes.
Bank Discount Yield • $10,000 par T-bill at $9,600 with 182 DTM. • $400(360/182) = $791.21thus the bank discount yield is 7.91% rBD=(10,000-P)/10,000 ·360/n • effective annual yield is: (1+400/9600)2-1=8.51% • bond equivalent yield is: rBEY=(10,000-P)/P ·365/n
Certificates of Deposit • Time deposits with commercial banks. • It may not be withdrawn upon demand. • Large CDs can be sold prior to maturity. • Insured by FDIC up to $100,000 (Federal Depository Insurance Corporation)
Commercial Paper • Unsecured short term debt (corporations). • Maturity is up to 270 days. • CP is issued in multiples of $100,000. • Small investors buy it through mutual funds. • Most issues have credit rating. • Treated for tax purposes as regular debt. • LC backed (letter of credit) optional.
Bankers’ acceptances • Orders to a bank by a customer to pay a given sum at a given date. • Backed by bank. • Traded in secondary markets. • Widely used in international commerce, because the creditworthiness is supplied by a bank.
Eurodollars • Dollar denominated time deposits in foreign banks. • Most are for large amounts and with maturity of less than 6 months.
Repos and Reverses • Repurchase agreements (RPs) used by dealers in government securities. • Term repo has a maturity of 30 days or more. • Reverse repo is the result of a dealer finding an investor buying government securities with an agreement to sell them at a specified price at a specified future date.
Federal Funds • Commercial banks that are members of the Federal Reserve System (Fed) are required to maintain a minimum reserve balance with Fed. • Banks with excess reserves lend (usually overnight) to banks with insufficient reserves.
Brokers’ Calls • Brokers borrow funds to loan to investors who wish to buy stock on margin. • The broker agrees to repay the loan upon the call of the bank. • The rate is higher because of the credit risk component.
LIBOR • London Interbank Offer Rate (LIBOR) is the rate at which the large London banks lend among themselves. • This rate serves often as an anchor for floating rate agreements which for example can be set at LIBOR + 3%
Yields on Money Market Instruments • In general, money market instruments are quite safe. • However, T-bills are the safest of the money instruments. • As a result the other instruments provide a slightly higher yield.
Fixed-Income Capital Markets • T-Notes - initial maturity of 10 years (or less). • T-Bonds - initial maturities of 10-30 years. • Par (also called face or principal) $1,000. • Interest (coupons) paid semiannualy.
Rate Mo/Yr Bid Asked Chg. Ask Yld 83/4 Aug 00n 105:16 105:18 +8 7.55 Rate coupon payment 83/4% of $1,000; paid semiannually; $43.75 per bond each 6 mo. Maturity = August 2000 n = note Bid =105:16 means 10516/32=105.5 at the price $1055 buyer is willing to buy. Ask=105:18 means 10518/32=105.5625 at the price $1055.625 seller is willing to sell.
Municipal Bonds (Munis) • Issued by state and local governments and agencies. Interest (not capital gains!) is exempt from federal taxes. • General Obligations are backed by the taxing power of the issuer. • Revenue bonds are backed only by revenues from specific projects. • Industrial Development bond is issued to finance a private projects.
Interest from Munis • Is not subject to federal income tax. • Hence the yields are lower: r (1- t) = rm r - before tax return on taxable bond rm - return on municipal bond t - marginal tax rate • Attractive to wealthy investors.
Corporate Bonds • Used to generate long-term funds. • The primary difference is the default risk. • Backed by specific assets (like mortgages). • By the financial strength of the firm only (debentures). • Callable at a call price (firm). • Convertible, may be exchanged to a stock (investor).
债券条款 • 信用 • 赎回条款 • 转换条款 • 回售条款 • 浮动利率
违约风险和评级 • 评级公司 • Moody’s Investor Service • Standard & Poor’s • Fitch (Duff and Phelps) • 两个大类 • 投资类 • 投机类
Investment Grade • Moody’s S&P=F • AaaAAA • Aa1 AA+ • Aa2 AA • Aa3 AA- • A1 A+ • A2 A • A3 A- • Baa1 BBB+ • Baa2 BBB • Baa3 BBB-
Speculative Grade • Moody’s S&P=F=D&P • Ba1 BB+ • Ba2 BB • Ba3 BB- • B1 B+ • B2 B • B3 B- • CCC+ • Caa CCC • CCC- • Ca CC • C C
评级机构使用的指标 • 偿债能力(Coverage ratios) • 杠杆比率(Leverage ratios) • 流动性比率(Liquidity ratios) • 盈利能力(Profitability ratios) • 现金流(Cash flow to debt)
违约风险保护 • 偿债基金 • 未来债务 • 红利限制 • 抵押
债券定价(Bond Pricing) PB = 债券价格 Ct = 利息 T = 付息次数 R = 要求收益率
10年期,面值1000, 8%息票率,半年付息一次 PB = $1,148.77 Ct = 40 P = 1000 T = 20 periods r = 3%
债券价格与要求收益率之间的关系 • 要求收益率高则债券价格低 • 要求收益率为零则债券价格为未来现金流之和
Price Yield 价格和要求收益率
10 年期,面值1000,息票率 = 7%,当前价格= $950 则,收益率r = 3.8635%
收益率折算 折算为年收益率 7.72% = 3.86% x 2 实际年收益率 (1.0386)2 - 1 = 7.88% 当期收益率 $70 / $950 = 7.37 %
实现的收益率和到期收益率 • 再投资假设 • 持有期收益 • 利率变化 • 利息的再投资 • 价格变化
持有期收益 I = 利息 P1 = 卖出价格 P0 = 买入价格
Example 息票率= 8% 要求收益率 = 8% 期限 =10年 P0 = $1000 由于要求收益率降到 7% P1 = $1068.55 HPR = [40 + ( 1068.55 - 1000)] / 1000 HPR = 10.85% (半年)
Accrued Interest • Additional payment for part of the coupon $ time
Price Quotes and Accrued Interest • Assume that the par value of a bond is $1,000. • Price quote is in % of par + accrued interest • the accrued interest must compensate the seller for the next coupon.
债券投资的基本策略 • 积极策略 • 预测利率走势 • 寻找市场的非有效性 • 消极策略 • 控制风险 • 平衡风险与收益
债券定价基本性质 • 价格和收益率的反向关系 • 收益增加比收益减少引起的成比例的价格变化较小 • 长期债券的价格比短期债券的价格对利率的敏感性更强 • 随着到期日的增加,价格敏感性的增加呈下降趋势 • 利率敏感性与息票率呈反向关系 • 当债券以一较低的到期收益率出售时,债券价格对收益变化更敏感
久 期 • A measure of the effective maturity of a bond • The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment • Duration is shorter than maturity for all bonds except zero coupon bonds • Duration is equal to maturity for zero coupon bonds
8% Time Payment PV of CF Weight C1 X Bond years (10%) C4 .5 40 38.095 .0395 .0198 1 40 36.281 .0376 .0376 1.5 40 34.553 .0358 .0537 2.0 1040 855.611 . 8871 1.7742 sum 964.540 1.000 1.8853 一个例子
久期与价格之间的关系 =连续复利 =年复利 修正久期D* = D / (1+y)