3. Convertible versus straight bond
Straight
bond
Pay 100 ... ... get 5% coupon each year ... ... get 100 back
Convertible
bond
Pay 100 ... ... get 3% coupon ... CHOICE:
... get 100 back
or take 10 shares
3080381l.ppt 2
4. Terminology explained
Conversion ratio Nominal amount Conversion Conversion
10 shares per bond ratio price
Number of shares
into which each
÷ =
bond converts €100 10 shares €10
Parity Conversion Today’s Parity
80% x =
ratio share price
Value of shares
10 €8 80%
underlying bond
Premium
25% Conversion Today’s Premium
Amount paid price share price
= +
above today’s
share price €10 €8 25%
3080381l.ppt 3
5. Convertible becomes equity if share rises
140 Bond issued at 100
on 25% premium
Bond price
Bond price / parity
Parity
100
Premium
80
50
Launch Year 1 Year 2 Year 3 Year 4 Year 5
3080381l.ppt 4
6. Convertible becomes a bond if share falls
140 Bond trends to 100
assuming issuer
not going bust
Bond price / parity
100
Bond price
80
Conversion value Premium
50
Launch Year 1 Year 2 Year 3 Year 4 Year 5
3080381l.ppt 5
7. Convertible payoff
Distressed Bond Hybrid Equity
CB value
Bond floor
Equity value
Stock price
3100356L.ppt 6
8. It works in reality too...
300
250
200
(%)
150
100
50
0
Nov-98 Jan-00 Mar-01 May-02
Parity FT 2% 2004
3080381l.ppt 7
9. Convertibles—two ways to think of them
Bond + Call Stock + Put
100
Option value Conversion
premium
80
60
(%)
Bond value Conversion value
40
(parity)
20
0
Bond “floor” moves with credit spread and interest rates,
parity moves with the stock price
3080381l.ppt 8
10. Convertible termsheet—checklist
Maturity Status / ranking Denomination
Issue price Coupon Redemption price
Conversion
Conversion ratio Conversion price
premium
Issuer call Investor put Exchange property
3080381l.ppt 9
12. The spectrum of products
Convertibles can be debt-like or equity-like
Equity
Mandatories
Reset
Conventional
Premium
redemption
Debt
3080381l.ppt 11
13. Premium redemption convertibles
♦ Price to buy convertible remains at 100
♦ Conversion ratio stays at 10 shares
♦ Zero coupon
♦ But backload missing interest payments to maturity
Pay 100 ... ... no coupon ... ... get 120 or 10 shares
(should be 3%)
3080381l.ppt 12
14. As well as convertibles, look out for …
♦ Issued by Company A (credit risk)
Exchangeables
♦ Converts into shares of Company B
(equity risk)
♦ E.g. News Corp. into BSkyB
♦ Guaranteed conversion into stock
♦ Very equity-like as no downside protection
Mandatories
♦ Pay high coupon, e.g. DT 6.50%
♦ Often exchangeable, e.g. Suez / Fortis,
FT / STM
3080381l.ppt 13
15. Modelling a CB
Inputs for bond value Inputs for option value
♦ Maturity ♦ Assumed volatility
♦ Issue price ♦ Dividend forecasts
♦ Coupon ♦ Stock price
♦ Redemption price ♦ Conversion premium / price
♦ Discount rate ♦ Call features
— interest rates
— credit spread
How to value prospectus risk / screws?
3080381l.ppt 14
16. CB valuation—outputs
“Simpler” outputs Model outputs
♦ Premium ♦ Theoretical value
— % difference between CB — What CB is “worth” if
price and parity inputs and model hold true
♦ Bond value ♦ Delta
— Discounted bond cash flows — Indicates equity short
ie ignores equity option hedge ratio
♦ Yield-to-maturity ♦ Implied volatility
— Rate of return of bond — Measure of “cost” of equity
cashflows option
“Cheap” and “Rich”are a matter of opinion
… thus making a market
3080381l.ppt 15
17. Implied volatility
♦ Most inputs for pricing are straightforward
— e.g. coupon, premium
♦ Some require some estimation
— dividends
— credit spread
♦ But the most disputed input is volatility
— discount to historic volatility
— volatility levels of comparable issues
♦ Once volatility is input, model calculates theoretical value (TV)
of CB
♦ Because inputs are so subjective market convention is to use
implied volatility
3080381l.ppt 16
18. Implied volatility
Implied volatility
♦ With all other variables fixed, what input volatility gives
theoretical value equal to issue price?
Worked example
♦ With input vol of 25, TV = 102.6
♦ Assume Tau = 0.65
♦ Implied volatility = 25 – 102.6 – 100.0 = 21.0
0.65
For outstanding issues, implied
volatility relates to current trading price
3080381l.ppt 17
19. Bond floor—worked examples
Worked example 1
♦ Discount rate 6%, CB coupon 4%, 5-year maturity
♦ What is bond value?
4 + 4 + 4 + 4 + 104 = 91.57
(1.06) (1.06)2 (1.06)3 (1.06)4 (1.06)5
Worked example 2
♦ Discount rate 7%, 3-year maturity
♦ What is coupon needed to get bond value of 90?
c + c + 100+c = 90
(1.07) (1.07)2 (1.07)3
c = 3.19% (or approximately 3.25%)
3080381l.ppt 18
20. Issuer call feature
Powerful tool for issuers to force conversion
♦ 5 year convertible with call after three years
♦ Issuer can redeem bonds early in 30 days’ time (at 100%)
♦ If parity above 100% investors would rather convert
♦ Soft call:
— bonds only callable if parity above e.g. 130%
— helps issuers extract better value from investors
— 30 day share price risk means some cushion needed anyway
3080381l.ppt 19
21. Rules of thumb—call feature
♦ 5-year maturity with NC3 (130%) most common today
♦ Why have a trigger?
— improves other terms versus unconditional call
— pragmatic “cushion” required to exercise unconditional call over
30 days, so might as well have trigger
♦ Call timing
— investors are wary of calls less than three years
— investors could lose a lot of option value if exercised
— but they may be key to meeting issuer’s needs
3080381l.ppt 20
22. Rules of thumb—premium redemption
♦ Yield to maturity 50bp more than conventional
♦ Premium unchanged
♦ Why?
— premium redemption less likely to convert
— investor needs compensation for lower option value
— investor needs compensation for lost coupon income
Zero coupon
♦ May need even more yield
♦ May need lower premium
♦ Dividend income loss effects more pronounced
3080381l.ppt 21
23. Rules of thumb—puts
♦ One-time option
♦ Allows investor to get money back before maturity
♦ Effectively shortens maturity
♦ Investors value to put date not maturity
♦ Smoke and mirrors tactic by banks
— give issuer and investor maturities they want
— long dated zero coupon deals issued at a discount
– e.g. Roche “US$3 billion” deal only raised US$1.2 billion
3080381l.ppt 22
24. A CB is not a bond plus warrants
♦ Can a CB be valued as a bond plus a call option?
♦ Whilst similar, the two are not the same
— investor bases different
— “usability” i.e. floating strike option
— warrants not callable
♦ CB pricing software more complex than Black-Scholes
3080381l.ppt 23
25. The Greeks
♦ Change in theoretical value for +1% change in stock
Delta ♦ Dictates stock to sell short to neutralise equity risk
♦ Typically 50–70% at issue
♦ Change in Delta for +1% change in stock
Gamma ♦ Positive number—Delta increases as stock rises
♦ Change in theoretical value for +1% change in volatility
Tau / ♦ Typically around 0.70
Vega ♦ e.g. 20% vol = 101.4% TV
21% vol = 102.1% TV
3080381l.ppt 24
26. Contact information
Martin Haycock
Head of Convertibles Marketing
Tel: +44-20-7568 2282
email: martin.haycock@ubs.com
Web pages: www.ubs.com
Bloomberg: UCBR,UCBI,UCBP
Reuters: CBMENU
UBS Limited
1 Finsbury Avenue
London, EC2M 2PP
Tel: +44-20-7567 8000
www.ubs.com
UBS Investment Bank is a business group of UBS AG
UBS Limited is a subsidiary of UBS AG.
3080381l.ppt 25
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and securities business group of UBS AG 3080381l.ppt 26
