Quantitative Methods - DCF Applications (cont.)

Continuing on with Quantitative Methods - DCF Applications.  Last we left we were looking at how to properly measure portfolio returns by using time-weighted over money-weighted rates of return.

Start - 1:15 pm

Quick recap on measuring portfolio rates of return

• The time-weighted approach is accomplished by finding what $1 invested at the beginning would return.  
• It is NOT affected by when people add money or take money away from the fund.  
• Therefore, to calculate it, you put in little walls anytime someone adds or withdraws from the fund.  Calculate the return between the adds/withdraws.  Basically, find the starting and ending value at each period.  
• Then to combine the returns simply multiply the (1+r) returns together to find what $1 invested at the beginning would have returned.  
• To annualize a quarterly return most accurately, you should compound it and not just multiply by four.
• The money-weighted return is not as good and also not as straightforward.  
• Essentially, you need to write an equation that puts ALL cash outflows on one side (and discounts them) and puts ALL cash inflows on the other side.  
• Simplify the equation combining like denominators in order to get all the terms on one side so that the NPV=0.  
• Then, you use your calculator to solve for the IRR (see my other post on this).

So a question: If, due to investor additions, you own more shares during a poor period, which measure will be higher, time-weighted or money weighted? * (answer at bottom)

So far we have not discussed risk in relation to return.  This will be an important topic going forward.  Before that though we must review some common conventions in the calculation and terminology of various measures of yield, our topic for this post.

Money Market Yields

• Can apply IRR and NPV in the short term debt markets
• Money Market - market for short term debt instruments, 1 year or less to maturity
• Some pay interest, others are pure discount
• US T-bill is the classic money market pure discount example
• Face value - how much the Government will pay you back
• Investors pay less than face and then receive the face
• Discount is face less amount paid
• This discount represents the interest the investor will receive
• Other money markets have their own conventions for quotes etc.
• Pure discount bonds are quoted on 'bank discount basis', which is a rate, not on price
• This annualizes the discount to face into an annual return
• Bank Discount Yield:
• rBD = D/F*360/t
• Where D is dollar discount, F is face, and t is number of days to maturity
• Note that annualizing like this assumes no compounding
• This yield is not meaningful tho, because:
• Based on face, not purchase price
• 360 (not 365) day year
• Annualizes with simple interest

Three more useful measures:

• Holding period yield - same as what we calculated for portfolios
• (P1 - P0 + D1) / P0
• In other words, price appreciation and interest divided by original price
• This accounts for accrued interest (interest that has accumulated but has not yet been paid because the bond traded between interest payment dates) because the accrued interest will be reflected in the purchase and sale prices
• D1 in a T-bill is zero because it is a discount instrument
• Effective annual yield - annualizes the HPY
• EAY = (1+HPY)^(365/t) - 1
• Note that this will always be higher than the bank discount rate assuming a positive interest rate because it compounds the rate
• Money market yield (aka CD Equivalent) - tougher equation - makes yield on a T-bill comparable to cash paying instruments that pay on a 360 day year
• Two ways to calculate
• rMM = HPY * (360/t)
• rMM = 360 rBD / (360 - (t)(rBD)
• This one is better because you don't need to know prices

Example

• You want to value a cashflow of $1,000 to be received in 150 days.
• You have data on the 150 day T-bill: HPY, Bank Discount Yield, Money Mkt Yield, and EAY.  Which can you use?
• Answer: HPY is easiest - discount period matches.  Do not use rBD because it is faulty.  For EAY and rMM, you need to readjust the period first to 150 days.
• Note - to shrink the EAY to a portion of the year, you use the reciprocal exponent
• EAYsmaller = (1+HPY)^(t/365) - 1 
• Further note - to shrink the rMM, divide it by the reciprocal (360/150)

Last note - converting periodic rates to annual rates

• Many bonds pay semiannual - IRR on a bond is called the Yield to Maturity
• If semiannual YTM is 4%, annual YTM is (1.04)^2 -1 = 8.16% (basically EAY)
• In the US bond market for some inexplicable reason they sometimes just double the semiannual YTM and call that the "bond equivalent yield" - this is so stupid - and even more stupid, in practice they just call this the bond's YTM

P 333-340 have practice problems which we will come back to.

End of Reading 6.

2:45 pm

About 1.5 hours (which felt like 3)

*Answer: Time-weighted.  The money weighted will attribute more of the return to the down period because you owned more shares during the down period.  Money-weighted is sensitive to both the timing and amounts of withdrawals and additions to the portfolio.