# pm

I have a question regarding PM Sml— capm is the slope of the sml… ok cml—sharp ratio is the slope of the cml… ok now is where I get all screwed up… what will cause the actual slope to change as opposed to a movement along the line? A question from bsas At the last FMOC meeting fed raised the fed funds rate by 25bps… Will this cause a shift in the sml or a change in the slope? The answer is shift. But whats the difference between a shift and a Change in the slope? I don’t get it…

think back to high school maths… the basic equation of a straight line: y = mx + b a change in m (the gradient) will change the slope (steepness) of the line a change in b (the y-intercept) will shift the line up or down if the fed raises the rate, how does this affect the SML/CML? it raises the risk-free rate (which is, in maths terms, the y-intercept)… so it will shift the line UP…

so what will cause the slope to change… not in math terms but in real termss…

actually, just re-reading that… my bad… if the question was related to the CML, then it would change the SLOPE… since the CML is the line the cuts the risk-free rate and is tangent to the efficient frontier… so, if the risk-free goes up, the line would cut the risk-free rate, but would touch the EF at a different market portfolio… or, in terms of the SML, a change in Beta would change the slope, since the formula goes: E®=RFR + Beta(E(Rm)-RFR)

the answer they give is it will shift the line… i also thought the slope

yeh i see what you’re saying…so really, an increase in the risk-free should change the slope AND shift the line… where did you get the question from? was it this years BSAS? morning or afternoon exam? and what question?

bsab 2006 pm dont have the book in front of me for the q #

ahhh yeh, i thought i’d seen it before…i also answered change in slope… but now that i think about it… i think the answer is a SHIFT… heres why: the SML equation is E®=RFR + Beta(E(Rm)-RFR), (where E(Rm) - RFR is the market premium), so we can rewrite as: E® = RFR + Beta(market premium) so, if RFR increases, you’d expect the expected return on the market to also increase, so that thr market premium is steady… thus, the only thing that changes in the equation if the RFR, thus causing a SHIFT in the SML

What causes the slope to change as opposed to movement along the line? ANS: If investors expect changes in market characterists, that is in terms of risk and rewards, then this will change the slope of the line. For example if they expect higher risk in the future they will then expect higher returns and this changes line slope. all portfolios are affected. The movement along the line happens for one particular portfolio if the risk of that portfolio increases or reduces while the entire market is still under the same premium as before. ie only that portfolio is affected.

thanks, but what about a change in the slope, as opposed to a SHIFT in the line?

If investors expect changes in market characterists, that is in terms of risk and rewards, then this will change the slope of the line. For example if they expect higher risk in the future they will then expect higher returns and this changes line slope. if originaly x= 1 and y = 2 after investors expect higher risk in the market they expect higher returns. This means a point of x = 1 may now equate to y = 4 (higher than original 2) Since intercept is still fixed at original RFR then the slope of line increases. The process is the opposite if investors expect low risks.

so if an individual co starts to increase its business risk… it should move along the SML. ? not shift the line b/c we are only dealing w/ one component of the graph… beta? and not looking at the y axis? expected return? so can i say that the slope will change when both the y and x are impacted>?

Correct about company changing its risk. Slope changes only if intercept remains same but y changes. x does not change.

Logically thinking 1.A shift in SML for example will be cause by a factor that affects all investments 2.A change in slope will be caused by a change in perspective relative to risk. If investors think they need to be rewarded more or less for an additional unit of risk they are taking then the slope will change 3.If an investment becomes more risky and returns more - movement along the line

thank you florinpop U have summarised so perfectly.

i can’t find anywhere in the cfa readdings that references the sharpe ratio as being the equivalent of the CML…? is it right to say that sharpe=CML?

i would say Sharpe ratio gives you the slope. because it states additional return per unit of risk

yeah, it seems like an obvious relo/tie together to have left out…

Logically thinking 1.A shift in SML for example will be cause by a factor that affects all investments 2.A change in slope will be caused by a change in perspective relative to risk. If investors think they need to be rewarded more or less for an additional unit of risk they are taking then the slope will change 3.If an investment becomes more risky and returns more - movement along the line now i got it… thanks easier to grasp…

florinpop, isn’t the sharpe ratio excess return over total portfolio risk. whereas the sml plots return to systematic risk (beta)