Exam ILA LAM Section A.1

r_t = (MV_t - MV_(t-1))/(MV_(t-1)) If CF occurs BOP t: (MV_t - (MV_(t-1) + CF_t))/(MV_(t-1) + CF_t) If CF occurs EOP t: ((MV_t - CF_t) - MV_(t-1))/(MV_(t-1)) Total rate of return - answer-Includes realized and unrealized capital gains in addition to income -Allows return to be compared across different types of investments -Became more popular after the 1960s *Higher asset volatility *Higher investor sophistication *Greater computing power time-weighted rate of return - answer-TWR = compound growth rate of $1 initially invested in the account Musst be calculated every time an external CF occurs Divide total period t into n sub-periods between external CFs (i = 1, 2, ..., n) r_(t,i) = (MV_i - CF_i) - MV_(i-1))/(MV_(i-1)) Chain-link the sup-period returns (r_(t,i)) TWR = Product of (1+ r_(t,i) - 1) 1 + r_(t,1) = "wealth relative" for sub-period 1, etc. money-weighted rate of return - answer-MWR = average compound growth rate of all money invested in an account (IRR) MV_T = MV_0*(1+R)^T + CF_t*(1-R)^(T-t) + CF_(t+1)*(1+R)^(t-(t+1) + ... MWR = (1+R)^T - 1 R = effective IRR per unit of time t There is usually not a closed form solution for R (must be solved for iteratively) TWR vs MWR - answer-Offsetting advantages and disadvantages Sensitive to size and timing of CFs: TWR-no MWR-yes Calculation freq required: TWR-High MWR-Low Admin expense and potential for error: TWR-High, MWR-Low Appropriate if manager has little/no control over external CFs: TWR-Yes, MWR-No MWR will diverge from TWR if there are large external CFs and/or high volatility Linked internal RAte of Return (LIRR) - answer-Blends advantages of TWR and MWR: 1.) Calculate MWR over reasonably frequent time intervals 2.) Chain-link the MWRs over the entire evaluation period LIRR is an acceptable proxy for TWR unless there are unusual circumstances -Unusual = large external CFs (10%+ of AV) an/or volatile account growth -Conclusion is based on a BAI study of monthly valuations and daily CFs Annualized Return - answer-Known as compound growth rate or geometric mean Data Quality Issues - answer-Reported rates of return are only as accurate as their inputs -Liquid, transparently priced securities have the most reliable returns -Thinly traded securities - could use matrix pricing *Estimate prices using dealer quoted prices for similar securities -Highly illiquid securities - carry at cost or price at last trade Report on a trade-date, fully accrued bases -Reflect impact of unsettled trades and income owed but not paid Current Yield - answer-only measures coupon income Current Yield = Annual Dollar Coupon Interest / Price Yield To Maturity - answer-IRR such that PV (CFs) = Price (or Initial Investment) -Typically expressed on a BEY basis (nominal semiannual) -Portfolio IRR can be calculated by combining all bond cash flows Yield to Call - answer-Like YTM but using a call date instead of maturity date Yield if bond is held until called at either 1.) First call date - date at which the bond can be called 2.) First par call date - date at which the bond can be called at par Total Return - answer-rate that accumulates full price and coupons to projected total future dollars at end of horizon Semiannual Total Return = (Total Future Dollars/Full Price of Bond)^(1/n) - 1 n = # of semiannual periods Yield Measures Compared - answer-Sources of bond return: 1.) Coupon interest: Current Yield-Yes, YTM/YTC-Yes, Total Return-Yes 2.) Capital Gain or loss: Current Yield-No, YTM/YTC-Yes, Total Return-Yes 3.) Interest-on-interest: Current Yield-No, YTM/YTC-Yes, but at YTM/YTC, Total Return-Yes None of the "conventional" yield measures accurately reflect all 3 sources. Interest-on-interest can be very significant (up to 80% of total return) Significance of Interest-On-Interest - answer--Can be very significant (up to 80% of return) -If reinvestment rates are less than YTM or YTC, total return <YTM or YTC -Characteristics that increase exposure to reinvestment risk: *Longer maturity dates *Higher coupons -Zero coupon bonds have no reinvestment risk if held to maturity Relationship Among Coupon, Current Yield, and YTM - answer-Bond Selling at: Relationship: Par coupon rate = Current yield =YTM Discount coupon rate < current yield < YTM Premium coupon rate > current yield > YTM "Discount" means the price < Par; "premium" is the opposite Yield-to-worst - answer-lowest possible YTC for any possible future call date -most conservative measure for a callable bond Problems with Yield to Call - answer-Problems in common with YTM 1.) Assumes coupons reinvested at YTC 2.) Assumes investor will hold bond to assumed call date Additional problems: 1.) Can't reflect reinvestment of proceeds at call date 2.) Assumes the issuer actually calls bond at call dates Floating Rate Bonds - answer-coupon fluctuates with reference rate R_t Coupon_t = (R_t + Spread) * Par Therefore, coupon values are unknown Discount margin - answer-estimated average spread over the reference rate for the life of the security Determining the Discount Margin - answer-Bond Selling at: Relationship Par Discount Margin = spread over ref rate Discount Discount margin > spread over ref rate Premium Discount Margin < spread over ref rate If selling at a premium or discount 1.) Determine future CFs assuming the ref rate never changes 2.) Select a margin (spread) 3.) PV the step 1 CFs at a discount rate equal to the ref rate + the spread in step 2 4.) Compare Step 3 to price -If the step 3 PV = price: discount margin = Step 2 spread -Else, try a different spread in Step 2 and repeat Evaluating Potential Bond Swaps - answer-1.) Pure yield pickup swap - replace a low yield bond with a higher yield bond 2.) Rate anticipation swap - takes advantage of an expected move in interest rates -If expecting rates to decrease, increase duration 3.) Intermarket spread swap - undertaken if manager believes yield spreads are mispriced by market -Bonds have differences in credit quality -Bonds have differences in features (calls, puts, etc.) 4.) Substitution swap - swapping bonds with identical features to get a bond with higher yield -Can result from capital market imperfection -Key risk: manager may be wrong to think bonds were identical Tax exempt municipals vs corporates - answer-Taxable equivalent yield = yield on a taxable bond that makes it equivalent to a tax exempt bond Taxable Equivalent Yield = Tax exempt yield/(1 - Marginal Tax Rate) Problems with taxable equivalent yield 1.) Same limitations as YTM 2.) Taxable and tax exempt bonds have different reinvestment opportunities - Only the coupon after taxes can be reinvested for a taxable bond -The full coupon of a tax exempt bond can be reinvested Solution: reflect changing tax rates in total return scenario analysis Types of Securities Issued by US Treasury - answer-1.) Discount securities (no coupons) -T bills have a maturity <= 1 yr 2.) Coupon securities -Notes have 2-10 year maturities -Bonds have maturities > 10 years (20- and 30- yrs) 3.) Treasury inflation protected securities -Principal is inflation adjusted by CPI -Coupons = fixed % of inflation adjusted principal 4.) Floating rate notes (FRNs) -2 yr, fixed principal notes that pay floating interest quarterly -Floating rate is based on 13 week t-bills The Primary Treasury Market - answer--Sold through sealed bid, single price auctions -Open to primary and non primary dealers *Primary dealers interact directly with NY Fed -Treasury accepts competitive bids from lowest to highest yield *Stops accepting when total issue (less noncompetitive bids) gets filled *Stop-out yield - highest yield accepted -Auctions are held on regular, predictable schedules -Treasury also exercises reopenings and buybacks *Reopening - additional offering of a security that is already outstanding *Buyback - when treasury buys outstanding Treasuries in the secondary market The Secondary Market - answer--Electronic, OTC, 24/7 market -Includes NY Fed open market operations -Trading activity volume 1.) On the run (69%) - most recently issued securities of a given maturity 2.) Off the run (27%) - older securities 3.) When issued (4%) - announced but not auctioned yet *Facilitates price discovery and competitive bidding Most trading activity is in Notes Quoting Conventions for Treasury Bills - answer-T-bills are quoted on a discount rate basis Y_d = (F-P)/F * 360/t F = face value P = price t = days til maturity Differs from standard return measures in 2 ways: 1.) Compares dollar return with face value instead of price 2.) Annualized using a 360-day year instead of 365 Points are split into 32ns and half 32nds (64ths); a "+" indicates an extra half 32nd -97-14 means 97 and 14/32 of par -97-14+ means 97 and 14.5/32 of par Bid/ask spreads range from 0.5-3.0 bps (tightest for actively traded issues) "Zeros" and "Strips" - answer-Created by stripping coupons and principal from issued Treasury securities -Not issued directly by Treasury Example: a newly issued 10-year note can be split into 21 individual securities: -20 semiannual coupons (Coupon strips) -The final principal payment (the principal stripp) STRIPS - Separate Trading of Registered Interest and Principal Securities -Created by Treasury in 1985 to improve liquidity of strips -Allows strips to be registered separately with Fed Govt Agency securities - answer-issued by fed govt agencies and GSEs -provides funding for home ownership and agriculture -similar in design to Treasury bills, notes, and bonds -Slightly more credit risk than Treasuries Largest active issuers are housing related - answer--Federal Home Loan Bank System (FHLB) -Federal National Mortgage Association ("Fannie Mae") -Federal Home Loan Mortgage Corporation ("Freddie Mac") Credit Quality of Agency Securities and Investors - answer-Agencies trade at slight discount to Treasuries, which reflects: -Strength of each agency's underlying business -Perceived govt backing (boosted by actions in the 2008 crisis) -Liquidity differences with Treasuries Agencies are attractive to investors who want: 1.) Slightly higher returns than Treasuries due to slightly higher credit risk 2.) Interest income (sometimes exempt from state and local taxes) Types of Agency Securities - answer-1.) Short dated (1-365 days) - "discount notes" priced like T bills 2.) Longer-dated (1-30 yrs) - pay semiannual coupons, like t-notes -Medium term notes (senior/subordinated, callable/putable, fixed/floating, etc.) -Step up notes - issuer can call at specific dates; else investor's interest rates increase 3.) FHLB TAP program - allows longer fixed-rate securities to reopen for 3 months 4.) FRNs - use a variety of indices, but SOFR is most popular 5.) Callable agencies (significant) -Helps manage mortgage prepayment risk from falling interest rates -Yield more than non-callable bonds -Main characteristics *Maturity date - latest maturity date if not called *Lockout period - initial period before agency can call *Type of call: -European - exercise only at end of lockout -Bermudan - exercise only at coupon dates after lockout -American - exercise anytime after lockout Primary Market - answer--Discount note auctions (short dated notes) -Reverse inquiries (all types) - investors can offer at "window rates" *Can result in non-standard issues (less liquid in secondary market) -Syndicated offerings (large, long dated securities) - group of dealers Secondary Market - answer--Multiple dealer, OTC (similar to Treasuries) -Mostly discount notes Issuing Agencies - answer-Fannie Mae and Freddie Mac -Created to develop/expand secondary mkt for residential mortgages -Both buy mortgages from lenders, then sell MBS or hold to maturity -Issue discount notes and medium term notes -Stockholder owned FHLB - network of 11 federally chartered private banks (biggest active issuer) -Supports residential mortgage, small business, rural, and agricultural lending -Not in conservatorship -FHLB Office of Finance - fiscal agent that issues "consolidated obligations" *Discount notes and bonds from $10M to billions -Member banks are jointly and severally liable Overview of Municipal Bonds - answer--Issued by states, local govts, and other public entities -Usually purchased for tax exempt status -Credit risk has increased in recent history Crossover buyer - answer-taxable bond investor that sometimes buys tax-exempt TCJA - answer-made munis less appealing to corporate investors Features of Municipal Bonds - answer--Coupons can be fixed, floating, or inverse floating -Some are issued originally at a discount to par (OIDs) -Serial bonds are common (multiple maturities per issue), but also term bonds -Legal opinion required to certify: *Issuer is legally able to issue bonds