I am really having a mental block in trying to get the mechanics of CPPI right. Can someone please help - here is where I am stuck: The guiding equation for portfolio rebalancing strategies is - Investment in stocks = m * (portfolio value - floor value) = m*cushion m = 1 — buy-and-hold strategy 01 – Constant percentage of portfolio insurance (CPPI) strategy So the text says that (1) the investor following CPPI has higher risk tolerance than others because he holds a multiple of cushion as stocks. (2) The floor value is dynamically adjusted as market prices fluctuate. Suppose my portfolio value is $100 with $60 invested in stocks and $40 invested in T-bills. So my floor value is $40. If I am following CPPI with m=1.2, investment in stocks should be $72. As a result, I sell T-bills and buy stock. Once I am done, I have $72 in stock and $28 in T-bills. However, this decreases my floor to $28, which would imply corresponding value of investment in stock is now 1.2 * ($100-$28) = $86.4. So you see, I am locked in a circular logic. Can someone please explain where am I going astray?
Here’s my take. You’re getting confused because you’re not making the distinction between PORTFOLIO value vs. equity value. in your example your portoflio was always worth $100. so your floor value should remain unchnaged. Using your original example. $100 equity, and $40 is your floor value. So your cushion is $60 (100-40). your m = 1.2 so you invest, as you stated $72 in equity. And that’s where you stop for the day. The next day your portfolio is worth, amazing, $200. Your floor value remains unchanged so your cusion has grown to $140. M = 1.2 so you invest $168 in equity.
I mislabeled the strategy - it is constant proportion strategy not constant percentage strategy. Striker, Page 371 of the CFAI text says “The floor in a buy-and-hold strategy is established with fixed investments in bills; in a CPPI strategy it is established dynamically.” I interpreted this to mean that floor changes with market value. However, I googled and found the following that supports your point that the floor is fixed and it is cushion that changes (which would make sense). Here is a numerical example I found: “let’s assume a portfolio of $100, a floor value of $75 and a multiplier of 2. As the initial cushion is $25 (100-75), the initial investment in stocks is $50 (25x2). Thus, the initial mix is 50/50 shares/cash. Suppose the sharemarket falls 10%, hence the investor’s shares will fall from $50 to $45. The total portfolio value is now $95, and the cushion is $20 (95-75). According to the CPPI rule, the new stock position is $40 (20x2). This requires the sale of $5 of shares and investment of the proceeds in cash.” My problem is that in above example I see inconsistency in numbers. If my floor is $75, that implies that I am holding $75 in cash. To that add $50 in stocks. This gives a portfolio value of $125, which is greater than $100 I have! Or, stated differently, if my initial mix is $50 in stocks and $50 in cash, than my floor is $50, not $75. I hope I am not being too dense here.
That’s where you need to wrap your thinking around that the floor does NOT equate to holding that amount in t-bills. That’s a fact. There’s no concept here i can demonstrate to you. The floor simply represents the worst your portfolio can do (assuming you have time to liquidate properly without adversly affecting the portfolio’s value). Meaning that going back to our example from before with a floor value of $40. at $100 portfolio value and a 1x multiplier (instead of our 1.2 before) you will hold $60 in equity. at $90 port value you’ll hold $50. $80 then $40 $70 becomes $30… $40 becomes zero…
Try this…with CPPI, the floor is a moving floor. Buy and hold is a constant floor
WS, not true. The floor value is the same with both CPPI and a buy and hold… The amount invested in equities and bonds changes with CPPI but only the amount of equity changes when investing in buy and hold.
strikershank Wrote: ------------------------------------------------------- > WS, not true. > > > The amount invested in equities and bonds changes > with CPPI but only the amount of equity changes > when investing in buy and hold. Hmmm. did I mis-express myself? According to what you said in second, it is exactly what I said, bond(floor)holding doesn’t change with buy-and-hold, hence constant floor. with CPPI, if investor is actively changing the equiyt and bond holding, then the bond(floor) value change, hence, moving floor. What did I miss?
The bond holding isn’t the floor…the floor is always $40 in the examples above…the floor doesn’t change and substituing the words bond for floor is inaccurate (so i think in your head you know what you’re talking about but it looks like there was a mis-expression) The bond and equity values change for CPPI while just the equity value changes for buy and hold.
Striker, I re-read your previous post 4 times…I am with you now. Thanks. Bad words on me.
CFAAtlanta Wrote: ------------------------------------------------------- > > “let’s assume a portfolio of $100, a floor value > of $75 and a multiplier of 2. As the > initial cushion is $25 (100-75), the initial > investment in stocks is $50 (25x2). Thus, the > initial mix is 50/50 shares/cash. Suppose the > sharemarket falls 10%, hence the investor’s shares > will fall from $50 to $45. The total portfolio > value is now $95, and the cushion is $20 (95-75). > According to the CPPI rule, the new stock position > is $40 (20x2). This requires the sale of $5 of > shares and investment of the proceeds in cash.” > > My problem is that in above example I see > inconsistency in numbers. If my floor is $75, that > implies that I am holding $75 in cash. To that add > $50 in stocks. This gives a portfolio value of > $125, which is greater than $100 I have! Or, > stated differently, if my initial mix is $50 in > stocks and $50 in cash, than my floor is $50, not > 75. I hope I am not being too dense here. I was just about to post this problem too.. I re-read the entire thread a couple of times but i'm just not understanding this: The value of the risk free assets (i.e the t-biils or cash as we are assuming zero return) is the floor of the portfolio - as stated on pg 368, cfai. So i'm not understanding striker's post. can anyone explain the above example from schweser?... i'm just not understanding it at all. why am i using 75 as floor to calculate stock investment if my floor turns out be 50$ (left over portfolio value after stock inv) Plus what am i rebalancing to ??? … the inv in both eq and floor in changing… the proportions are changing… what am i doing ?
I just googled and i think i have understood it - a bit… forget about floors and cushions and tapestry… here is how i interpreted it: You decide a minimum value for your portfolio. say, you have a 100$ port and you can’t afford to have your portfolio fall below 75$… you need at least 75$ - now in a constant mix strategy, you would invest 75$ in cash/t-bills and leave it at that. However in CPPI, you think in terms of total portfoilio value- as long as your port is 75$ you are happy. You decide on a ‘m’ that is how much you want to invest in stocks. this figure will depend on your risk tolerance. say you decide on a multiple of 2. Total port value= 100 You want it to remain at least 75 cushion= 25 now as you can take on more risk (m=2) … you invest 25 x 2 = 50 in stocks and the rest in bills/ cash. Now lets say, the stock market falls 10%, and your shares are reduced in value to 45$ … your portfolio value falls down to 95 ( 45 in shares + 50 in bills ) not good… so now you have to reduce your exposure to equity… 95-75 = 20 20 x2 =40 and the remaining in bills… so you shift money to bills and now bills = 55$ Suppose an extreme case, that your portfolio is now worth only 75$ … not good… this is the minimum you wanted… so now you can’t take on any risk… whatever allocation you may have had in shares prior to this, you sell it off and invest it all in risk free bills. the problem i think is that before we were thinking in % and proportions… CPPI thinks in terms of dollar value of portfolio Thats how i interpret it… is it right ? … any problem anywhere ?
also, say m=1 … thats your eq investment… ( 25 in eq and 75 in bills ) …with m=1, you can lose all of your eq and still not affect your minimum value… m=2 … ( 50 in eq and 50 in bills ) … you can lose 50% of your eq value and still not affect your minimum value … -> 50% loss = 25 left in eq and 50 in bills… anything more than that and your portfolio value falls below the acceptable amount. m=3 … (75 in equity and 25 in bills )…you can lose only 33% (approx) of your eq value and still not affect your minimum value … -> 33% loss = 50 left in eq and 25 in bills… anything more than that and your portfolio value falls below the acceptable amount i think as m increases… you need to monitor your portfolio more… the more risk you take on (higher eq investment) … the more sensitive your portfolio becomes to market movements (obviously)
bips, that sounds right
Thank you… I get it.
sounds exactly like everything that was posted above before the extra long posts.
A related question to the above topic: Schweser (in Schweser ProQBank to Study Session test 7, Q2, last part) writes: “With a constant mix strategy, an investor’s risk tolerance is constant, regardless of wealth levels.” CFAI (Vol 5, p. 370) writes: “A constant mix strategy is consistent with a risk tolerance that varies proportionately with wealth”. Later they elaborate and say “it is constant relative risk” compared to the level of wealth. Any ideas ho to interpret? Thanks.
CM has constant “relative” risk tolerance because you are always trying to hold the same percentages of cash and stock. It has increasing “absolute” risk tolerance as the market increases because the overall portfolio value (and stock value within the portfolio) is increasing. B&H and CPPI also have increasing “absolute” risk tolerance as the market increases, and they both have increasing “relative” risk tolerance as well because the percentage of stock in the portfolio also grows.
bips, I totally bought into what you were saying, but then I read CFAI book 5, page A-29 in paragraph (iii) about CPPI. “and the value of that floor is invested in some nonfluctuating asset (eg. Tbills or money market)”
TooOld4This Wrote: ------------------------------------------------------- > bips, > > I totally bought into what you were saying, but > then I read CFAI book 5, page A-29 in paragraph > (iii) about CPPI. > > “and the value of that floor is invested in some > nonfluctuating asset (eg. Tbills or money market)” Yes, this is exactly what has bothering me - I sent an email to CFAI yesterday requesting a review.
I think the way it works even though the value of the floor is inversted in T-bills (which are nonfluctuating according to CFAI, in practice they will have little fluctuation), but anyway, as the value of your protfolio is rising during rising stock morket, and you need to hold more stocks in your portfolio according to CPPI, you readjust it by selling T-bills and buying stocks (i.e., the value of the floor doesn’t stay fixed).