جميع الكتب

مهني

1 Markets I: The Ecosystem and Exchange-Traded Marketsالأسواق عبر الإنترنت 2 Markets II: Rates, FX and Creditالأسواق عبر الإنترنت 3 Markets III: Commodities, Energy and Cryptoالأسواق عبر الإنترنت 4 Quantitative Methodsالأساليب عبر الإنترنت 5 Derivatives and Volatilityالمشتقات عبر الإنترنت 6 Rates, Credit, XVA and Riskالفائدة والائتمان والمخاطر عبر الإنترنت 7 Research Craft: Predictors, Backtests, Measurement, Portfoliosالبحث عبر الإنترنت 8 Strategies I: Equities and Futuresالاستراتيجيات عبر الإنترنت 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desksالاستراتيجيات عبر الإنترنت 10 Microstructure and Executionالتنفيذ عبر الإنترنت 11 Market Making and High-Frequency Tradingصناعة السوق عبر الإنترنت 12 Machine Learning for Marketsتعلم الآلة عبر الإنترنت 13 Low-Latency Softwareالتكنولوجيا عبر الإنترنت 14 Networks, Hardware and Trading Infrastructureالتكنولوجيا عبر الإنترنت 15 Research, Data and Risk Platformsالتكنولوجيا عبر الإنترنت 16 The Desk and the Firmالشركة عبر الإنترنت 17 The Industry: Firms, Roles and Careersالمسارات المهنية عبر الإنترنت 18 The Interview Bookالمسارات المهنية عبر الإنترنت
التطبيقات حول المدرب تسجيل الدخول ابدأ القراءة

Quantitative Finance · المسرد

ما معنى Discount, money-market and bond-equivalent yields؟

يُعرف أيضًا باسم: discount yield · money-market yield · bond-equivalent yield

Definition 2.2 Markets II: Rates, FX and Credit · الفصل 2 — Money Markets

For a bill with tt days to maturity and price PP per 100 of face value: the discount yield dd (bank discount basis) is the discount expressed on the face value over a 360-day year, P=100 (1−d t/360)P = 100\,(1 - d\,t/360); the money-market yield m=100−PP360tm = \frac{100 - P}{P}\frac{360}{t} is simple interest on the amount paid over a 360-day year, the rate of a deposit of the same term; the bond-equivalent yield ii (the Treasury’s investment rate) is the same on a 365-day year, i=100−PPyti = \frac{100 - P}{P}\frac{y}{t} with y=365y = 365, or 366 if the year after issue contains a 29 February, for bills of at most half a year; beyond half a year it solves

P[1+(t−y2)iy](1+i2)=100,P\Bigl[1 + \Bigl(t - \frac y2\Bigr)\frac{i}{y}\Bigr]\Bigl(1 + \frac i2\Bigr) = 100,

a semiannual compounding that makes it comparable with the yield of a coupon bond (Chapter 3).

One illustrative bill curve (the seven auctioned maturities) in the three conventions. Discount yields fall steadily with maturity; money-market yields do not, because the gap between them widens with the term: the 52-week bill yields more than the 26-week in that convention. Only the bond-equivalent curve can be joined to the coupon curve. Levels are illustrative, not quotes. Data: the chapter’s tutorial.
Figure 2.1. One illustrative bill curve (the seven auctioned maturities) in the three conventions. Discount yields fall steadily with maturity; money-market yields do not, because the gap between them widens with the term: the 52-week bill yields more than the 26-week in that convention. Only the bond-equivalent curve can be joined to the coupon curve. Levels are illustrative, not quotes. Data: the chapter’s tutorial.

أمثلة

Example 2.4 (A thirteen-week bill)

A 91-day bill auctioned at a discount rate of 3.82% costs 100(1−0.0382×91/360)=99.034389100(1 - 0.0382 \times 91/360) = 99.034389 per 100. Its money-market yield is 3.8572% and its bond-equivalent yield 3.9108%: nine basis points separate the number on the auction screen from the number to compare with a Treasury note. The formulas are the Treasury’s own, and they reproduce its published examples to the last digit (Section 2.6).

اقرأ في الفصل →