This document provides an overview of convertible bonds, including: 1) Key terms like conversion ratio and conversion price as well as how the price of a convertible bond is calculated. 2) The hybrid characteristics of convertibles that provide downside protection like bonds and upside potential like equities. 3) Metrics used to analyze convertibles such as delta, gamma, and cheapness. 4) An example of a hypothetical Concerto-FS convertible bond is presented to demonstrate these concepts.

1. Sasan Mansouri
Concerto University
July 2016
www.Concerto-fs.com

2.  Introduction to convertible bonds
 Price Behaviour of Convertible bonds
 Special Properties of Convertible bonds
 Bloomberg guide for Convertibles
 Convertible Bonds Indecies
 Bank CoCo

3.  A Normal Bond with a specific “option”
 Option: give up the coupons received from the bond in exchange for a fixed number of
shares of common stocks of a company
 The value of a convertible bond = MAX(Bond , Stock)
 Hybrid Asset with:
 Downside protection of Bonds
 Upside return of Equities

4. For Investors For Corporations
• Higher Yield than corresponding Equity
• Bigger value of the corresponding Bond
(Bond Floor)
• Option to Convert to Equity if Equity price
raise
• Case the stock price falls,
• Cheaper way of financing (Lower coupon
rates)
• The company can defer equity financing to
a time when growth has been achieved

8.  𝐶𝐵 𝑣𝑎𝑙𝑢𝑒 = 𝐵𝑜𝑛𝑑 + 𝐶𝑎𝑙𝑙 𝑂𝑝𝑡𝑖𝑜𝑛
 𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒(𝐼𝑉) = 𝑡=1
𝑇 𝐶𝑜𝑢𝑝𝑜𝑛
(1+𝑅𝑖𝑠𝑘𝐹𝑟𝑒𝑒𝑅𝑎𝑡𝑒+𝐶𝑟𝑆𝑝𝑟𝑒𝑎𝑑) 𝑡 +
𝑃𝑎𝑟𝑉𝑎𝑙𝑢𝑒
(1+𝑅𝑖𝑠𝑘𝐹𝑟𝑒𝑒𝑅𝑎𝑡𝑒+𝐶𝑟𝑆𝑝𝑟𝑒𝑎𝑑) 𝑇
 𝐶𝑎𝑙𝑙 𝑂𝑝𝑡𝑖𝑜𝑛 = 𝑆𝑡 × 𝑅 × 𝑒−𝑞(𝑇−𝑡) × 𝑁 𝑑1 − 𝐼𝑉 × 𝑒−𝑅𝑖𝑠𝑘𝐹𝑟𝑒𝑒𝑅𝑎𝑡𝑒 𝑇−𝑡 𝑁 𝑑2
 𝑑1 =
𝐿𝑛
𝑆 𝑡 𝑅
𝐼𝑉
+(𝑅𝑖𝑠𝑘𝐹𝑟𝑒𝑒𝑅𝑎𝑡𝑒−𝑞+
𝜎2
2
)(𝑇−𝑡)
𝜎 𝑇−𝑡
 𝑑2 = 𝑑1 − 𝜎 𝑇 − 𝑡
 𝑆𝑡 = current stock price
 R = Conversion Ratio
 T = Expiration time
 q = dividend rate
 N() = Normal cumulative distribution function

11.  Example of Concerto-FS Convertible Bond:
CFS 4.5% Convertible 20 years ISIN: DECFS0012345
Stock Price 20 € per share in DAX
Stock dividend 0.5 € per share
Par Value (Issue Price) 100 € (issued at par)
Convertible Bond Price 76.35 € (Today price in secondary Market)
Conversion Ratio 3.454
Conversion Price (Strike price) 100/3.454= 28.95 € per share
Theoretical Price(Assume inputs …) 74.45 €
Call Features Hard Call 3 years
Soft Call 140% trigger
Put Features No
Maturity 20 years Coupon 4.5% (Semi annual Frequency)

12.  Conversion Ratio = 3.454 So, each bond can be converted to 3.454 shares
 Parity = Conversion Ratio * current share price
 Absolute Premium = (Convertible Bond Price - Parity)
 Premium = (Convertible Bond Price - Parity)/Parity
 Current Yield = Coupon/Current Price of Convertible
 Convertible Yield Advantage = Current Yield - Dividend Yield
 Break even (years) = Absolute premium / Convertible Yield Advantage
 Delta = (
𝜕 𝐶𝐵.𝑃𝑟
𝜕 𝑆𝑡.𝑃𝑟
) ; Gamma = (
𝜕 𝐷𝑒𝑙𝑡𝑎
𝜕 𝑆𝑡.𝑃𝑟
) ; Vega = (
𝜕 𝐶𝐵.𝑃𝑟
𝜕 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦
)
 Cheapness = (Market price – Theoretical Price) / Market Price

14.  Quarterly rebalancing : second Wednesday in January, April, July and October
 The FX rates used during the Quarterly Index Reselection are the FX rates at the
Reselection Reference Point
 Constituent number : nearly 218
Region Threshold >=
US US$300m
Europe US$200m
Other US$200m
Asia US$100m
Japan US$100m
Outstanding Issue Proceeds Requirement
Maturity
Breakdown
Weight %
0 - 1 Year 7.60
1 - 3 Years 29.05
3 - 5 Years 36.63
5 - 7 Years 14.06
7 - 10 Years 4.90
10 - 20 Years 3.83
> 20 Years 3.94

15. Sector Breakdown Weight %
Technology 35.91
Consumer Non-Cyclical 16.91
Consumer Cyclical 14.31
Capital Spending 11.22
Financial 7.95
Basic Materials 4.84
Energy 3.87
Utilities 3.61
Other 1.38
Credit Quality
Breakdown
Weight %
AAA 1.63
AA 0.33
A 9.09
BBB 14.05
BB 15.08
B 6.63
CCC 0.53
NR 52.66
Delta Breakdown Weight %
Bond-like (0 to 25) 20.04
Hybrid (25 to 60) 47.66
Equity-like (Over 60) 30.67
Cash 1.63
Top Country Weights Weight % Top Country Weights Weight % Top Country Weights Weight %
United States 38.36 Italy 2.76 Portugal 1.04
Japan 10.46 Spain 1.66 Norway 0.9
France 7.95 South Africa 1.48 Sweden 0.83
Germany 6.76 CASH 1.37 Mexico 0.7
China 5.88 Singapore 1.3 Malaysia 0.67
UK 4.13 Hungary 1. 16 Israel 0.47
Netherlands 3.84 Taiwan 1. 13 Greece 0.45
Hong Kong 3.33 UAE 1.04 Other 2.33

16.  After Financial Crisis 2008 the idea controlling banks raised.
 Instead of Bailing Troubled banks out; Some proposals for Bail-in came out.
 For case of Europe, BRRD regulation framework.
 CoCos are part of Bail-in able asset that help troubled banks to recapitalize.

22.  DRD/QDI eligible means that the income that the security pays is eligible for a
reduced tax rate if the investor qualifies.
 DRD refers to corporate owners (Just for corporations that are taxed separately
from their owners)
 QDI to individuals
 A security of certain quality can be DRD or QDI eligible; which means, its
dividends contains some tax reduction

23.  Example: Assumes a 35% tax rate for the corporation receiving the dividend.
 For a corporate: Taxable income =
Taxable income before DRD(income + dividends(from other stocks)) – DRD amount
Percent
Ownership
Dividends Received
Deduction(DRD)
Implied Tax Rate
on Dividends
< 20% 70% 10.5% [= 35% × (1-70%)]
20 - 80% 80% 7.0% [= 35% × (1-80%)]
> 80% 100% 0.0% [= 35% × (1-100%)]