Concepts Description
Fixed‐Income Portfolio Management : Introduction
Roles of fixed‐income securities 1. Diversification : low correlation to equity
2. Regular predictable CF
3. Inflation hedge :
‐ Inflation‐linked bonds : both coupon and principal are inflation protection
‐ Floating‐coupon securities : coupon are inflation protected, but not the principal
Fixed‐income Mandates 1. Liability‐based mandates : portfolio assets solely to meet expected future liability payouts
Immunisation : all CF reinvested until paid out to meet liabilities
‐ CF matching : CF occur when and in size needed to meet liabilities payouts
‐ Duration matching : match duration of assets and liabilities → assets and liabili es fluctuate @ same % as interest rate change → ending value match
‐ Contingent immunization :
+ Portfolio funded with more money than required to meet future liability payout. PV of assets ‐ PV of liabilities = surplus
+ Manager could manage portfolio to add value. If sucess → surplus grow. If unsuccessful, and surplus ≤ 0 → immunize por olio
‐ Horizon matching : combine CF and duration matching to fund multiple future liabiliites. ST liabilities are CF matched ; LT liabilities are duration matched
2. Total return mandates : target an absolute rate of return or equal / outperform an index
Key metric : Active return
‐ Pure indexing : replicate performance of a bond index. Target 0 active risk and return
‐ Enhanced indexing : allow some flexibility in construction → seek small ac ve return (20 → 30 bps). Dura on is matched ; but risk is mismatched (over / underweight sector)
‐ Active management : allow large deviations from risk factors of the index → seek greater ac ve return (+50 bps)
Liquidity Liquidity : ability to make transaction in large size, quickly, with minimal deviation from market price of asset
Reasons for liquidity issues :
‐ Great variety of different bond issues, each with small amount (an issuer could have different bond outstanding, with unique terms, coupon and call features). Bond are
heterogeneous (unlike stock, which is homogeneous)
‐ Bonds are usually traded OTC → more cost to find + less transparent
Liquidity varies by bond market sector :
‐ On‐the‐run developed‐market G‐bond (recently issued) : more liquid
‐ C‐bond : liquidity decline as quality (bond is riskier)
Effect of liquidity :
‐ Pricing data : difficult to find pricing info
+ Matrix pricing : YTM of recent trades with similar features (maturity, quality, coupon) is used to calculate price of similar bond
‐ Portfolio construction :
+ Buy & hold : need less liquidity → may prefer less liquid bonds for higher yield
+ Active : prefer more liquid
‐ Trading done in dealer market. Less liquid bonds → longer me for dealer to sell → higher bid/ask spreads
Alternatives :
‐ Derivatives : bond futures (exchange traded), interest swaps (OTC)
‐ ETFs
Fixed‐income returns model
𝐵𝑜𝑛𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑌𝑖𝑒𝑙𝑑 𝑖𝑛𝑐𝑜𝑚𝑒 𝑅𝑜𝑙𝑙𝑑𝑜𝑤𝑛 𝑟𝑒𝑡𝑢𝑟𝑛 𝑃𝑟𝑖𝑐𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦𝑖𝑒𝑙𝑑 𝑐𝑢𝑟𝑣𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑙𝑜𝑠𝑠𝑒𝑠 𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝐺/𝐿𝑙𝑜𝑠𝑠
In which :
𝑌𝑖𝑒𝑙𝑑 𝑖𝑛𝑐𝑜𝑚𝑒 𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 / 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒
𝑅𝑜𝑙𝑙𝑑𝑜𝑤𝑛 𝑟𝑒𝑡𝑢𝑟𝑛 𝐸𝑛𝑑𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 / 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒
1
𝑃𝑟𝑖𝑐𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦𝑖𝑒𝑙𝑑 𝑐𝑢𝑟𝑣𝑒 𝑀𝑜𝑑𝐷𝑢𝑟 ∆𝑌 𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 ∆𝑌
2
𝐶𝑟𝑒𝑑𝑖𝑡 𝑙𝑜𝑠𝑠𝑒𝑠 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠𝑒𝑠
Leverage Leverage : to increase portfolio return
‐ Interest rate < Return on portfolio assets → gain
‐ Interest rate > Return on portfolio assets → loss
‐ Asset duration > Liability duration (Borrow at shorter‐term interest rates → cost increase faster than return on assets if interest rates increase)
𝑉
𝑟 𝑟 𝑟 𝑟
𝑉
In which :
𝑟 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜
𝑟 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑎𝑠𝑠𝑒𝑡𝑠
𝑟 𝑏𝑜𝑟𝑟𝑜𝑤𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑉 𝐴𝑚𝑜𝑢𝑛𝑡 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑
𝑉 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑
Methods to achieve leverage 1. Repurchase agreemets (Repos) : Securities owners "sell" a security for cash + agree to "buy" back at specified future date
‐ Securities "sold" = collateral
‐ Haircut = MV of collateral ‐ Loan ammount (This is not the interest)
2. Futures contracts :
𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑀𝑎𝑟𝑔𝑖𝑛 𝑎𝑚𝑜𝑢𝑛𝑡
𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒
𝑀𝑎𝑟𝑔𝑖𝑛 𝑎𝑚𝑜𝑢𝑛𝑡
3. Swap agreements : Receive fixed rate + pay floating rate = Buying bond + Borrow money @ floating rate
4. Structured finance instruments :
‐ Example : inverse floater ‐ Buy GBP10m 6‐year (20% ‐(4 x LIBOR) = buy GBP50m 4% 6‐year bond + borrow GBP40m at LIBOR floating rate
5. Securities lendings : to support short‐selling
, Risks of leverage ‐ Interest rate risk : interest rate > return of portfolio assets → loss
‐ Fire sale : Increase interest rate → Decrease value of leveraged por olio and collateral → money lenders demand repayment + force liquida on of por olio assets → selling under
dustressed
Manage taxable and tax‐exempt Types of tax issues :
portfolios ‐ Coupon payment and capital gain are taxed differently
‐ Capital gain is taxed at sale → gain on longer period securi es may be taxed at lower rate than shorter period securi es
‐ Capital losses could be used to offset capital gains only
‐ Possible to invest some portion of portfolio in tax‐sheltered / tax‐advantages accounts
Strategies to manage taxable account :
‐ Realise capital losses to offset capital gain
‐ Extend holding periods to realise LT capital gain
‐ Extend holding periods to defer tax
‐ Consider differentials in income tax rates vs. capital gain tax rates when selecting investments
Taxation of investments in mutual funds : Income is taxable when earned by the fund
‐ Some countries use pass‐through taxation of gains : fund investor is taxed when fund realises gain, but that tax payment reduces tax on gains when sell fund shares later
‐ Other countries use deferred taxation of gains realised within the fund : tax investors when fund shares are sold
Fixed‐Income Portfolio Management : Introduction
Roles of fixed‐income securities 1. Diversification : low correlation to equity
2. Regular predictable CF
3. Inflation hedge :
‐ Inflation‐linked bonds : both coupon and principal are inflation protection
‐ Floating‐coupon securities : coupon are inflation protected, but not the principal
Fixed‐income Mandates 1. Liability‐based mandates : portfolio assets solely to meet expected future liability payouts
Immunisation : all CF reinvested until paid out to meet liabilities
‐ CF matching : CF occur when and in size needed to meet liabilities payouts
‐ Duration matching : match duration of assets and liabilities → assets and liabili es fluctuate @ same % as interest rate change → ending value match
‐ Contingent immunization :
+ Portfolio funded with more money than required to meet future liability payout. PV of assets ‐ PV of liabilities = surplus
+ Manager could manage portfolio to add value. If sucess → surplus grow. If unsuccessful, and surplus ≤ 0 → immunize por olio
‐ Horizon matching : combine CF and duration matching to fund multiple future liabiliites. ST liabilities are CF matched ; LT liabilities are duration matched
2. Total return mandates : target an absolute rate of return or equal / outperform an index
Key metric : Active return
‐ Pure indexing : replicate performance of a bond index. Target 0 active risk and return
‐ Enhanced indexing : allow some flexibility in construction → seek small ac ve return (20 → 30 bps). Dura on is matched ; but risk is mismatched (over / underweight sector)
‐ Active management : allow large deviations from risk factors of the index → seek greater ac ve return (+50 bps)
Liquidity Liquidity : ability to make transaction in large size, quickly, with minimal deviation from market price of asset
Reasons for liquidity issues :
‐ Great variety of different bond issues, each with small amount (an issuer could have different bond outstanding, with unique terms, coupon and call features). Bond are
heterogeneous (unlike stock, which is homogeneous)
‐ Bonds are usually traded OTC → more cost to find + less transparent
Liquidity varies by bond market sector :
‐ On‐the‐run developed‐market G‐bond (recently issued) : more liquid
‐ C‐bond : liquidity decline as quality (bond is riskier)
Effect of liquidity :
‐ Pricing data : difficult to find pricing info
+ Matrix pricing : YTM of recent trades with similar features (maturity, quality, coupon) is used to calculate price of similar bond
‐ Portfolio construction :
+ Buy & hold : need less liquidity → may prefer less liquid bonds for higher yield
+ Active : prefer more liquid
‐ Trading done in dealer market. Less liquid bonds → longer me for dealer to sell → higher bid/ask spreads
Alternatives :
‐ Derivatives : bond futures (exchange traded), interest swaps (OTC)
‐ ETFs
Fixed‐income returns model
𝐵𝑜𝑛𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑌𝑖𝑒𝑙𝑑 𝑖𝑛𝑐𝑜𝑚𝑒 𝑅𝑜𝑙𝑙𝑑𝑜𝑤𝑛 𝑟𝑒𝑡𝑢𝑟𝑛 𝑃𝑟𝑖𝑐𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦𝑖𝑒𝑙𝑑 𝑐𝑢𝑟𝑣𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑙𝑜𝑠𝑠𝑒𝑠 𝐶𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝐺/𝐿𝑙𝑜𝑠𝑠
In which :
𝑌𝑖𝑒𝑙𝑑 𝑖𝑛𝑐𝑜𝑚𝑒 𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 / 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒
𝑅𝑜𝑙𝑙𝑑𝑜𝑤𝑛 𝑟𝑒𝑡𝑢𝑟𝑛 𝐸𝑛𝑑𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 / 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒
1
𝑃𝑟𝑖𝑐𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦𝑖𝑒𝑙𝑑 𝑐𝑢𝑟𝑣𝑒 𝑀𝑜𝑑𝐷𝑢𝑟 ∆𝑌 𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 ∆𝑌
2
𝐶𝑟𝑒𝑑𝑖𝑡 𝑙𝑜𝑠𝑠𝑒𝑠 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠𝑒𝑠
Leverage Leverage : to increase portfolio return
‐ Interest rate < Return on portfolio assets → gain
‐ Interest rate > Return on portfolio assets → loss
‐ Asset duration > Liability duration (Borrow at shorter‐term interest rates → cost increase faster than return on assets if interest rates increase)
𝑉
𝑟 𝑟 𝑟 𝑟
𝑉
In which :
𝑟 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜
𝑟 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑎𝑠𝑠𝑒𝑡𝑠
𝑟 𝑏𝑜𝑟𝑟𝑜𝑤𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
𝑉 𝐴𝑚𝑜𝑢𝑛𝑡 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑
𝑉 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑
Methods to achieve leverage 1. Repurchase agreemets (Repos) : Securities owners "sell" a security for cash + agree to "buy" back at specified future date
‐ Securities "sold" = collateral
‐ Haircut = MV of collateral ‐ Loan ammount (This is not the interest)
2. Futures contracts :
𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑀𝑎𝑟𝑔𝑖𝑛 𝑎𝑚𝑜𝑢𝑛𝑡
𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒
𝑀𝑎𝑟𝑔𝑖𝑛 𝑎𝑚𝑜𝑢𝑛𝑡
3. Swap agreements : Receive fixed rate + pay floating rate = Buying bond + Borrow money @ floating rate
4. Structured finance instruments :
‐ Example : inverse floater ‐ Buy GBP10m 6‐year (20% ‐(4 x LIBOR) = buy GBP50m 4% 6‐year bond + borrow GBP40m at LIBOR floating rate
5. Securities lendings : to support short‐selling
, Risks of leverage ‐ Interest rate risk : interest rate > return of portfolio assets → loss
‐ Fire sale : Increase interest rate → Decrease value of leveraged por olio and collateral → money lenders demand repayment + force liquida on of por olio assets → selling under
dustressed
Manage taxable and tax‐exempt Types of tax issues :
portfolios ‐ Coupon payment and capital gain are taxed differently
‐ Capital gain is taxed at sale → gain on longer period securi es may be taxed at lower rate than shorter period securi es
‐ Capital losses could be used to offset capital gains only
‐ Possible to invest some portion of portfolio in tax‐sheltered / tax‐advantages accounts
Strategies to manage taxable account :
‐ Realise capital losses to offset capital gain
‐ Extend holding periods to realise LT capital gain
‐ Extend holding periods to defer tax
‐ Consider differentials in income tax rates vs. capital gain tax rates when selecting investments
Taxation of investments in mutual funds : Income is taxable when earned by the fund
‐ Some countries use pass‐through taxation of gains : fund investor is taxed when fund realises gain, but that tax payment reduces tax on gains when sell fund shares later
‐ Other countries use deferred taxation of gains realised within the fund : tax investors when fund shares are sold
