Synthetic equity / synthetic cash

A small part of this I have struggled to grasp on both my run throughs of the chapter: Schweser bk 4 pg 117 - explains that to convert cash to syntetic equity you must multiply by the risk free rate before dividing by the futures value (and multiple) which makes sense to me. However in the lower example on page 121 when converting synthetic cash to sythetic equity no mention of risk free rate is made (only the current value of the synthetic cash is used). If a risk free rate (and a time frame) were given should they have been used? Synthetic cash is calculated in this section by reducing the beta to 0 or reducing the duration to the cash duration. Does synthetic cash created via these methods actually yield the risk free rate? If not, then I guess that would explain why no risk free rate was used.

first, if you believe CAPM (r = rfr + beta * erp), then a security with beta equal to zero is risk free. but, if you dont, then the argument doesn’t hold. (think of it mathmtically, a taylor expansion to an unknown process, it’s first derivative can be zero, but non-zero in higher orders) . but, i think cfai would like us to believe CAPM explains the “nature” of security return. i.e. there’s no higher order uncertainties. second, it’s a little triky for bonds because the current bond theory involves the 2nd order derivative, convexity (r = rfr - d * delta + c * delta ^ 2). by reducing the 1st order derivative, the duration, to zero, it doesn’t guarantee a risk-free. but, given the approach is a simple point estimate, and also one can assume interest rate changes in a very tight range such that higher order term can be ignored, with these assumptions, you do get risk free. the real math involved in asset allocation and rebalance is more complex (multiple risk exposure, higher order changes, optimizations, … etc) than those showing on schweser. but, the book does teach us the essence of the process.

Who says something with beta = 0 is risk-free? CAPM doesn’t say that; it says it has 0 systematic risk. A Van Gogh has beta = 0 but is hardly a risk-free investment.

JoeyDVivre Wrote: ------------------------------------------------------- > Who says something with beta = 0 is risk-free? > CAPM doesn’t say that; it says it has 0 systematic > risk. A Van Gogh has beta = 0 but is hardly a > risk-free investment. 1st, the discussion was in the context of portfolio rebalance process, i.e. we were talking a well diversified portfolio, not a van gogh. so, u r taking this out of context. 2nd, for a well-diversified portfolio, capm identifies only one risk, the market risk. so, r = rfr + b * erp. u can say this is wrong by citing fama french. but, with capm being “true”, if a manager reduces the porfolio’s beta to zero, he earns risk-free rate. even in this portfolio, van gogh happens to be in its constitutents. the argument still holds as long as market portolio includes paintings auction market.

Damosin99 Wrote: ------------------------------------------------------- > A small part of this I have struggled to grasp on > both my run throughs of the chapter: > > Schweser bk 4 pg 117 - explains that to convert > cash to syntetic equity you must multiply by the > risk free rate before dividing by the futures > value (and multiple) which makes sense to me. > > However in the lower example on page 121 when > converting synthetic cash to sythetic equity no > mention of risk free rate is made (only the > current value of the synthetic cash is used). If a > risk free rate (and a time frame) were given > should they have been used? I think the Rf is mentioned ---- the 3-month Treasuries yielding at 2.8%, which is the Rf you are looking for. Schweser has also used this 2.8% to come up with the FV of $10,069,276.78 in 3 months. > Synthetic cash is calculated in this section by > reducing the beta to 0 or reducing the duration to > the cash duration. Does synthetic cash created via > these methods actually yield the risk free rate? yes, I think so. > If not, then I guess that would explain why no > risk free rate was used. I don’t get this point … - sticky

Thanks Sticky. The risk free rate of 2.8% is mentioned in the earlier example but my point was that it was not used (or even mentioned) in the latter example (where synthetic cash was converted to synthetic equity. This was what I was struggling with.

rand0m Wrote: ------------------------------------------------------- > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > Who says something with beta = 0 is risk-free? > > CAPM doesn’t say that; it says it has 0 > systematic > > risk. A Van Gogh has beta = 0 but is hardly a > > risk-free investment. > > 1st, the discussion was in the context of > portfolio rebalance process, i.e. we were talking > a well diversified portfolio, not a van gogh. so, > u r taking this out of context. > > 2nd, for a well-diversified portfolio, capm > identifies only one risk, the market risk. so, r > = rfr + b * erp. u can say this is wrong by > citing fama french. but, with capm being “true”, > if a manager reduces the porfolio’s beta to zero, > he earns risk-free rate. even in this portfolio, > van gogh happens to be in its constitutents. the > argument still holds as long as market portolio > includes paintings auction market. This is just not true nor is it anywhere in CAPM. Suppose I hold $1M worth of the market portfolio and short 1.7M worth of beta =1.7 Electric Underwaer Corp. Do you think CAPM say I have a riskless portfolio? It might say I expect the rf rate, but it is a highly suboptimal way of getting it.

JoeyDVivre Wrote: > > > This is just not true nor is it anywhere in CAPM. > Suppose I hold $1M worth of the market portfolio > and short 1.7M worth of beta =1.7 Electric > Underwaer Corp. Do you think CAPM say I have a > riskless portfolio? It might say I expect the rf > rate, but it is a highly suboptimal way of getting > it. u took this discussion out of context again. the question in the schweser book is about shorting futures of the “same underlying”. the base risk is in different section. if u wanted to bring other risk exposure into this discussion, u should have clarified. for the example u raised, as long as u choose to short 1M of market portfolio, u r risk-free. (btw, shorting 1.7M of beta=-1.7, doesn’t seem to hedge 1m of market portfolio at all. i assume they were typos. u shouldn’t expect rf either given the significant base risk introduced) by the way, it is fine for you to think that i am dead wrong. but, my “wrong” idea would handle this exam on this subject just fine.

I think the logic is: If you have an asset (or combination of assets) with 0 risk, you get the risk free rate (usually)*. That doesn’t mean that any asset or combination with zero market risk (i.e. beta=0) gets the risk free rate, since there may be ideosyncratic or asset-specific risks that still exist. These risks are not (usually) paid, so it is conceivable that the expected return will be risk free (this is not required, but possible), but it is no sense actually risk free. * - Exceptions are where there is a true arbitrage opportunity, however this should be eroded away fairly quickly in an efficient market. Another possibility is that something is riskless but gets less than the risk free rate, in which case, it is more profitable to just buy riskless assets instead and forget about the other one. In theory, this means that those assets should eventually dwindle to 0 because no one will want them (but human sentimentality is likely to mitigate this to some extent).