 Now, let's see what effect will be on the CML and the SML if any of the assumptions related to the KPM are relaxed. We know that the KPM assumes boring and lending at the same risk-free rate, but in real world we see it is impossible to lend and borrow at the same risk-free rate. So we see two different lines going to the Markovitz efficient frontier. The first line risk-free rate F that is R, FR, F shows investment opportunities that combining the risk-free assets and the portfolio F on Markovitz efficient frontier. Now it is impossible to extend this line without further borrowing at RFR or the risk-free rate to acquire further units of F at the same level of riskiness. So in order to get more units of F, we need to have borrowed some amount at the rate of RB in order to invest in portfolio K so that we can extend our CML along the line segment KG. This means that now CML is made up of RFR, K and G that is it is a line segment of RFRF and we have now a curve segment which is RFR, which is FK and another line segment that is KG and that KG is possible to the additional borrowing at the RB. So we see that as we have the slope of the borrowing line KG lesser than the slope of RFRF. So in this case the investor is at the loss means his net return is the loss because the slope of KG is lower than the slope of RFRF. The assumption to relax the risk-free rate means we have a zero beta model. In this case if portfolio M is a mean variance efficient portfolio that is an alternative model by black which does not require a risk-free asset. In this case within the asset of feasible alternative portfolios many exist where returns can completely uncorrelated with the market portfolio. In this case the beta of these portfolios with the portfolio M is zero. So zero beta portfolio does not have any systematic risk however it may have some unsystematic risk. The availability of zero beta portfolio will not affect the CML but it will allow the construction of a linear CML as we can see this line in the diagram. A zero beta capital model can also be presented like the regular capital model. In this model we have an equation where expected return on security i is equal to the expected return on a zero bitum. This is the zero rate of return and it replaces the risk-free rate. In replacement of RFR we use the term RZ so we see that zero beta model generally does not require any risk-free asset. The KPM model also assumes no transaction cost but if we assume that there exists some transaction cost then the investor will buy as the KPM assumes no transaction cost so investor will buy or sell any missed price security until they plot them on the security market line but if there exist any transaction cost the investor will not try to correct the missed pricing because in this case the cost of buying and selling the missed price security may exceed any potential access return which will investors return into loss so the securities will plot very close to the SML as we can see in the diagram securities are plotting alongside this thick line at a interval with the transaction cost SML will be a band of securities rather than a straight line so we see that we have a band between these two lines above the SML and below the SML this means that the width of this band is basically a function of the amount of the transaction cost. Heterogeneous expectations and the planning periods investors with different expectations about risk and the expected return would definitely have a unique CML and the SML on on individual basis we know that KPM is a one period model so corresponding to the planning period for every individual investor a one year planning period the KPML the CML and the SML would also differ for someone with a one month planning period so if we have an expectation difference difference and the timing difference the CML and SML will also be differing for individual investors taxes KPM assumes no taxation but in real corporate world taxes are there means that the expected return in the KPM are pre tax return as we have seen earlier in the model whereas the actual return for most of the investors are after tax if we see this model this model provides the returns after the deduction of capital gain tax which is levied on the capital gain or the price appreciation and in the other part of the equation we see a tax on the dividend so we are taxing two items for the return the first tax is on the capital gain that is the price appreciation and the second tax is on the dividend receipt tax rates differ between individuals and and corporations or the institutions for institutions that do not pay taxes the pre-tax model is correctly specified because their pre-tax and after tax gains are the same in this way we can say that tax rates can cause major difference in the CML and the SML among the investors whether they are individual investors or the institutional investors