Risky Asset and Risk Free Asset

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dinesh.sundrani

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RA = Risky Asset
RFA = Risk Free Asset
CORR(RA, RFA) = COV(RA, RFA)/ [STD(RA) * STD(RFA)]
It’s known to us that Covariance of risk-free-asset with the risky asset is 0 i.e. COV(RA, RFA) = 0 and Risk Free asset have literally no risk, so STD(RFA) = 0
does that mean CORR(RA, RFA) = 0/0 = Indeterminate ???
if no, then what do we assume the Correlation of risk free asset with the risky asset ?? 0?
- Dinesh S
STALLA PASSMASTER says this “The correlation between a risk-free asset and a risky asset is zero, not negative.”
 
to sum it up:
std(rfa)=0
cov(ra,rfa)=0
thus
corr(ra,rfa)=0
but indeed, as you derived: 0/0 is an indeterminate - but I would do not bother with that right now..
 
Thanks barthezz, just wanted to confirm it with the experts. You summed up E(Rp) and VAR(P) pretty well too (in the other thread).
-Dinesh S
 
barthezz and dinesh
this was discussed before
the idea that there is no linear relationship between RFR and a risky asset not that there couldn’t be any other type of relationship. and it makes sense since they both should have a small impact on economy that would affect each other, just that the impact might be too small and hard to determine as a formula
 
florinpop,
i have some difficulties interpreting your lines.
are you saying that the “mixture” risky portfolio + risk free asset does not result in a linear function of the std (portfolio)?
 
sorry barthezz
i meant that the correlation between a risky asset and the Risk free asset is not necessarly inexistent but simply is not a linear one.
 
there is correlation between a risky portfolio and risk free asset and that correlation is ZERO.
that is basically the idea of CML - you add to a risky portfolio a risk free asset and what you get is a straight line.
 
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