Value of floor does not stay fixed - there is contradiction in terms here. What good is floor if it keeps decreasing each time stock prices drop? I had reconciled to following picture but now it is up again in the air - Target equity allocation = m X (Portfolio value - Floor value) = mX Cushion Initial investment $100. Desired floor value $40. m=1.2 ==> $72 in stocks an $28 in T-bills. Stocks drop 50% to $36 ==> Portfolio value = $36+$28 = $64 and Cushion = $64- $40 = $24. ==> new allocation to stocks = $1.2 X 24 = 28.8 and T-bills = $64 - $28.8 = $35.2 So as strategy demands, we sell stock as stock prices go down.
Not sure what is troubling you. In CPPI, you sell stock as as prices go down (value of floor goes up) and you buy stock as prices go up (value of the floor goes down). When you reach a point when the portfolio value is equal to floor value, the allocation to stock goes to 0. This is where “insurance” of CPPI comes into play, as you are guaranteed that the portfolio value won’t drop below floor value. If you compare CPPI to constant mix, which offeres no protection of the downside. The value of portfolio in constant mix can go to 0, if m=1 (i.e., it was fully allocated to stocks) and stock market crashed.
value of floor is fixed… but value of t-bills fluctuates based on total value of portfolio and m value. floor value does not equal t-bill value (unless m=1) i think the issue here is that in the cfai answer that TooOld4This quoted states that floor value = t-bills
volkovv, there are two schools of thought here for CPPI - one says floor value is fixed and is a separate number from the investment in T-bills. The second says the floor varies and is same as the investment in T-bills. Can you illustrate your answer with a numerical example (that is, if you care and have time)? Start with $100 to invest, Floor of $40 and m = 1.2.
I think the whole confusion here is the definition of the floor, think of it as two way to describe the floor (i.e. initial floor and current floor). Floor(1) is the initial floor or the minimum acceptable value of your portfolio, lets say investors says, I won’t tolerate for my portfolio to drop below $40, then $40 becomes the floor, this value will always stay fixed and you will use it in CPPI formula to calculate the value invested in stock. Floor(2) is how much you are currently invested in rissk-free asset (i.e, T-bills). This value equals: Portfolio value - Value of stock; floor(2) will keep changing as the value of your stock position chnages. When portfolio value equals to floor(1), floor(2) = floor(1), and value of stock position is 0. Hope this makes it clear.
our messages got crossed, here is an example: at t=0 Portfolio value = $100 Floor = $40 m=1.2 Value of stock = 1.2 * (100 - 40) = 72 Value of T-bills = 100 - 72 = 28 at t=1 Portfolio value = $150 Floor = $40 m=1.2 Value of stock = 1.2 * (150 - 40) = 132 Value of T-bills = 150 - 132 = 18 at t=2 Portfolio value = $60 Floor = $40 m=1.2 Value of stock = 1.2 * (60 - 40) = 24 Value of T-bills = 60 - 24 = 36 at t=3 Portfolio value = $40 Floor = $40 m=1.2 Value of stock = 1.2 * (40 - 40) = 0 Value of T-bills = 40 - 0 = 40
Oh then we are on the same page… your floor 1 is not changing as well and your calculations are same as mine few posts above. And I celebrate the birth of floor 2!
So volkovv what you’re saying is that there is an errata on pg. A-29? Atlanta, is that what you asked CFAI for clarification on? Let us know if they reply.
i don’t think its an errata, i just needs to be interpreted differently they say “…floor is invested in some nonfluctuating asset (e.g., Treasury bills or money market funds)” what they are trying to say, the value of the floor is not changing, if it is left alone (i.e., the asset is not growing through price appreciation), I suppose they are saying not growing above what is normal (i.e., risk-free rate) however, once you buy or sell additional T-bills to maintain CPPI strategy, the value of the floor will change, but not through price appreciation but through increasing/reducing the position dedicated to T-bills
volkovv Wrote: ------------------------------------------------------- > the value of the floor > will change, but not through price appreciation > but through increasing/reducing the position > dedicated to T-bills But the position in T-bills changes because of price appreciation, seems like circular argument. I think it all boils down to what is the definition of floor.
I am not disputing that position in T-bills is not changing, T-bills are growing at risk-free rate, so price appreciation exists. I was trying to explain what they meant by “nonfluctuating assets”, i.e., they are assuming there no wild swings in T-bill’s price beyond risk-free rate; both, price appreciation of equities and risk-free rate appreciation of T-bills contribute to increase/decrease of portfolio value, and that is taken into an account when calculating new CPPI value of stock upon portfolio rebalancing going back to numeric example at t=0 Portfolio value = $100 Floor = $40 m=1.2 Value of stock = 1.2 * (100 - 40) = 72 Value of T-bills = 100 - 72 = 28 at t=1 Portfolio value = $150 Floor = $40 m=1.2 Value of stock = 1.2 * (150 - 40) = 132 Value of T-bills = 150 - 132 = 18 between t=0 and t=1, portfolio grew from $100 to $150, lets say stocks grew by $48 and T-bills grew by $2. So we have stock at t0 = 72 T-bills at t0 = 28 Portfolio value = 100 stock at t1 (before rebalancing) = 72 + 48 = 120 T-bills at t1 (before rebalancing) = 28 + 2 = 30 Portfolio value = 150 CPPI rebalancing tells us that stocks should be 132 and T-bills should be 18, so we sell 12 worth of T-bills and buy 12 worth of stock.
I understand your point about “nonfluctuating assets” and Tbills growing at Rf. That’s a red herring, it’s not my beef with that quote from A-29. What I was trying to point out (and I think CFAAtlanta is too) is that CFAI says that the “investor sets a floor below which he does not wish assets to fall, and the value of that floor is invested in…Tbills…”. Later in that paragraph, it says that CPPI is “…appropriate for an investor who has zero tolerance for risk below the stated floor…”. I can’t reconcile what you describe to be CPPI (and by the way I agree that this is how it works) with these statements! In your example, you end up with a floor of $40 and Tbills of $18. This doesn’t sound like zero tolerance for risk below $40 to me.
What CPPI says is that the value of the portfolio will never fall below the floor, which is set at the beginning, $40 in our example. It doesn’t say that position in T-bills in any point in time can’t be below the floor. For a moment assume that you are going to rebalance daily (to avoid significant drop in equity before you had a chance to rebalance in the declining market). When market is going up, CPPI gives you a chance to participate in the up market, and that comes at the expense of lowering position in T-bills. But in the up market you are not worried about downside, assuming you constantly monitor your portfolio, and can rebalance when situation reverses. When your portfolio reaches $240, the value of T-bills will drop to $0 (i.e., 1.2 * (240 - 40) = 240). If portfolio will keep going up, then you will start borrowing at tisk-free rate (shorting T-bills) to be able to have higher position in equities. As soon as the market will start going down, you are going to cut on equitites and put more and more in T-bills. When the portfolio will reach $40, you will have $0 in equities and $40 in T-bills, and at this point portfolio won’t be going down any longer, since you only have a risk-free position.
What you describe makes alot of sense in practice. But in theory, the “risky asset” can drop to zero before you can react. (Remember they only use equities as an example of a risky asset – what if your risky asset was widget futures – can you still say that daily monitoring will prevent the portfolio from dropping below $40?) Someone with a zero-tolerance for dropping below $40 should always have $40 invested in Tbills. Period. I still believe that yourdescription of the CPPI method is correct, and that CFAI has an error on page A-29.
Agreed that risky asset can drop to zero in theory before you have a chance to react, but I think whole strategy works in a way that the risky portion of your portfolio is diversified in some way, thus greatly reducing chances of such an event happening (but nevertheless therisk is still present). The more riskier and less diversified the risky assets are, the more frequent monitoring and rebalancing would be, heck, maybe you can have some algorithm that rebalances dynamically, if you don’t care about transaction costs. But, if such risk is still not tolerable by you, you either won’t take much risk in your risky portfolio, or choose buy-and-hold or constant mix strategy, where the minimal value of risk-risk free asset is guaranteed. But for the exam purposes, all we need to be concerned about is how to calculate CPPI as we discussed above and what its advantages/disadvantages are.
I got an email from CFAI saying their Curriculum Department (or such) is investigating my views regarding the problem solution on page A-29 and will get in touch with me soon.