Financial Markets (Bilingual Teaching)
investors to convert the bond into a specified number of common stock shares; Investors will accept a lower yield for convertible bonds because investor returns include expected return on equity participation
6) The appropriate yield to be offered on a debt security is based on the risk-free rate for the corresponding maturity plus adjustments to capture various security characteristics Yn = Rf,n + DP + LP + TA + CALLP + COND Where:
Yn = yield of an n-day security Rf,n = yield on an n-day Treasury
(risk-free) security
DP = default premium (credit risk) LP
= liquidity premium
TA = adjustment for tax status CALLP = call feature premium COND = convertibility discount 2. Theories Explaining Shape of Yield Curve 1) Pure Expectations Theory
Long-term rates are average of current short-term and expected future short-term rates; Yield curve slope reflects market expectations of future interest rates; Forward rate:
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Financial Markets (Bilingual Teaching)
market’s forecast of the future interest rate
? Upward-Sloping Yield Curve: Expected higher interest rate levels; Expansive monetary policy; Expanding economy
? Downward-Sloping Yield Curve: Expected lower interest rate levels; Tight monetary policy; Recession soon?
2) Liquidity Premium Theory
? Investors prefer short-term, more liquid, securities; ? Long-term securities and associated risks are desirable only with increased yields; ? Explains upward-sloping yield curve 3) Segmented Markets Theory
? Theory explaining segmented, broken yield curves ? Assumes investors have maturity preference boundaries, e.g., short-term vs. long-term maturities
? Explains why rates and prices vary significantly between certain maturities
3. Calculation based on theories of term structure of interest rates ( esp. “Pure Expectations Theory” & “Liquidity Premium Theory” )
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Financial Markets (Bilingual Teaching)
附件：纯预期理论的数学表达
长期利率相当于在该期限内人们预期出现的所有短期利率的平均数。基于即期利率和远期利率的关系推导如下。
如下图所示：现在时点为0，凡是以现在时点算的利率均为即期利率，即R0,1~R0,5；其余均为远期利率，如R1,2表示起点为1终点为2的1年期利率，其他以此类推（如R2,4表示起点为2终点为4的2年期利率等等，图中没有标出）：
R0,1 0 1 R1,2 2 R2,3 3 R3,4 4 R4,5 5 R0,2 R0,3 R0,4 R0,5
如果从0时点起，投资者用1元钱要投资5年，显然投资者有多种选择，根据“无套利”思想，各种选择方案之间应该没有差别，即终值应该相等。
关注两种特例，即“一步到位”（现在持有一直到5年末），另外一种是每次投资1年也到5年末，则两方案终值相等，按照一般复利（或非连续性复利，Compound Interest/ Discrete Compound Interest）：
(1?R0,5)5?(1?R0,1)(1?R1,2)(1?R2,3)(1?R3,4)(1?R4,5)
两边取对数，有：
5ln(1?R0,5)?ln(1?R0,1)?ln(1?R1,2)?ln(1?R2,3)?ln(1?R3,4)?ln(1?R4,5)
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Financial Markets (Bilingual Teaching)
如果1元钱投资1年（利率为R），按照一般复利计算终值为（1?R）；如果以连续复利（Continuous Compound Interest）计算（即“利滚利”，时间无限细分）且设定连续复利的利率为r，则终值为er。 同样根据无套利思想有：1?R?er?r?ln(1?R)。 据此，结合前述分析有如下结论：r0,5?r0,1?r1,2?r2,3?r3,4?r4,55。
如果投资者不是5年投资期限，可以扩展到一般情况。 进一步思考：“一步到位”、“5年投资逐年滚动”仅为两种典型的投资方案，尚有其他多种方案可以满足“如果从0时点起，投资者用1元钱要投资5年”的要求，由于这些方案之间是无套利的，据此计算0～5年内其他远期利率，如：
投资者可以选择先投资2年再投资3年，且终值与“一步到位”
1)是一样的，即（一般复利）：1(?2R,(025,2)?1R(35,0?)?R5
，可以据此计算
?35?r按照上述思路肯定有（连续复利）：22r,05,25,r0r2,5，即以2年为起点以5年为终点的远期利率可以计算出来。
纯预期理论认为，以某时点为基础确定的收益率曲线形状完全取决于投资者对未来的预期；如果投资者预期远期利率将走高（如经济趋于繁荣），那么根据上述等式，长期即期利率将大于短期即期利率，收益率曲线将上翘，反之则相反。
要求：（1）掌握按照一般复利进行计算的情况；（2）掌握按照连续复利进行计算的情况；（3）各种期限的远期利率计算均需要掌握。
注意：如果涉及计算，请务必看要求是基于“一般复利”还说“连续复利”。
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Financial Markets (Bilingual Teaching)
Chapter4 Money Markets
1. Money Market Securities:
Maturity of a year or less; Debt securities issued by corporations and governments that need short-term funds 2. Treasury Bills
1) T-bills represent the simplest form of borrowing: The
government raises money by selling bills to public. 2) Investors buy the bills at a discount from the stated
maturity value.
3) At the bills maturity, the holder receives from the
government a payment equal to the face value of the bill. 4) T-bills with initial maturities of 91 days or 182 days are
issued weekly.
SP?PP365*5) Calculating T-Bill Annualized Yield: YT? PPn6) Calculating T?bill discount?3. Commercial paper
Par?PP360* PPn1) Large, well-known companies often issue their own
short-term unsecured debt notes rather than borrow directly from banks.
2) Commercial paper is backed by a bank line of credit.
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