 Bismillahirrahmanirrahim. We are starting financial risk management and in that we are starting portfolio risk management. So lastly we were discussing that how portfolios can be evaluated that mean if you have more than one portfolio how to decide which one to select and in that context we learned one method as we discussed there many method we learned about shop ratio that we can rate portfolios or rank portfolios based on sharp ratio and if I can briefly recall that is the excess return over the risk-free rate divided by the standard aviation. Then as I told you there are many other ways when another more frequently used method is the trainer ratio. These ratios are actually evaluating things and then they suggest us the conclusion to invest or to make a decision out of. Trainers is also named after the guy who invented it that is Jack Lay trainer and it's used to my year returns and specifically used to rank the portfolios in this context. It is the risk earned in excess which it could not be earned over the investment so again it is risk earned in access to risk-free rate but which is similar to the shop ratio but we'll also do a comparison of what trainer and shop are different other differences but the first part is pretty similar in both the context but what difference trainer comes in trainer differentiate the risks in two categories. We have discussed different types of risk and one category was systematic and unsystematic risk so we'll be also spending more time on that when we were looking at in graphical way as well. So when we say systematic risk systematic risk is about the market. You can refer to the topic systematic and unsystematic risk for better understanding of this point but here for our assumption we need to know that trainer capture only systematic risk and the higher again the rule is same higher the trainer ratio better the portfolio is. Formula for trainer ratio is the return minus risk-free rate as you can relate it we call it which very similar to shop ratio but the denominator is a bit different here we have beta beta or people call it beta but beta is no more than I only use so in shop ratio we were using sand aviation here we are using beta beta is a mayor of systematic risk it only take care of the systematic risks which are available or part of the investment or the portfolio. So it's even simple words that as much as we take systematic risk against how much access return we are getting this trainer ratio calculates. We will also calculate it with figures but the broader understanding is that as much as we take systematic risk against how much access return we got. Risk-free rate assumption again I'll tell you that when you are investing in risk-free rate then you are not taking any risk so when you are taking access risk or adopting systematic risk then how much access return you are getting. Taking the equation detail above let's assume that expected portfolio return is 20% or risk-free rate is 5% and the beta of the portfolio is 1.5 so as simple logic 0.2 is expected return minus 0.05 which is the risk-free return divided by the denominator that is 1.5 so it gives us the trainer ratio of 0.1 again referring to the logic of ratios and the factors that these are not telling anything concrete in isolation. When we have two different portfolios we calculate trainer for both of them and based on that analysis we make a decision. How the trainer ratio works? Trainer ratio attempt to measure how successful investment is in providing compensation to investor for taking the investment risk. The risk we are taking gives us what the portfolio is offering because when we are taking a risk we should be compensated for that particular risk trainer is reliant upon portfolios beta beta is the sensitivity of the portfolio with the markets that is being gauged through the beta so this is purely in the calculation of systematic risk how the trainer ratio work is the premise behind ratio is that investor must be compensated for the risk inherent to portfolio because diversification will not remove it here the important point is that the systematic risk will not end with diversification i.e. if we increase the number of security, increase the pool of portfolios, increase the class then the systematic risk will not be reduced. The end result is the unsystematic risk so this risk will stay so when this risk is to be here then investor should also get his gist return so higher that is the better that would be so what is the key takeaway of the trainer module? The higher the trainer ratio portfolio is more suitable the more comparison we are doing, the more portfolio we are comparing so the trainer ratio should be more suitable for us it is similar to sharp ratio sharp ratio that you have analyzed yourself that sharp ratio is quite similar with few differences the only main factor is that the risk calculation and the risk context are different in both ratios but overall mechanism is somewhat very similar but everything is not perfect this ratio also has some limitation or points which we need to be cautious and carefully looked at the main weakness is it is backward looking backward looking means it is related to the past past is taking data based on past calculation we are deciding that investments are likely to perform and behave differently in future basic calculation we can link from past but there is no rule that past is going to repeat historians keep saying that history is bound to repeat but in finance we do not adopt it because if for one period returns dynamics are calculated that's not necessary that they will be the same in the next period we can estimate them or forecast them but having this assumption that this exact repeat that's not true so this is the limitation of this ratio is it's dependent on appropriate benchmark to measure beta how to calculate beta we will refer to this point in the illustration but a common phenomenon is that garbage in garbage out if you do not put the input right then the output will not be right so if your beta calculation is not right then the output of the trainer and the ranking of the trainer will be affected additionally there is no dimension upon which to rank the trainer ratio when comparing similar investment higher trainer is better but there is no definition of how much better it is than the other so this is basically relatively better but how much better it is how much output will be better it is not absolute so it is not absolute it is a relative measure of telling that this portfolio can be gauged case we will refer to it and discuss it we will have a better idea case one if portfolio has a return of 12 percent and beta is 1.4 and the risk we return is 2 percent so you can easily calculate that the trainer ratio is 12 minus 2 divided by 1.4 the beta so the round answer is 7.4 is the 10.1 4 is the trainer ratio considering assuming that all the other factors remain the same only changes that beta 1 so what will happen 12 minus 2 divided by 1 so the trainer ratio comes to be 10 you can see that it moved from 7 to 10 when our beta changed here two points are going to understand the first thing is that portfolio 2 is definitely better because it has a higher trainer ratio so if we have two choices then we will select this 2 that it is giving us a given low level of risk return here what I was going to say is that both the return is 12 and both the access return is 10 so then how is the difference here it's beauty of you finance people who you are Mashallah educated children of finance here they can understand and tell people a lot they can explain that it is not just a return matter what is the matter here risk adjusted return given level of risk who is giving us a better return both were getting 10 but in one place only one beta we get that return in the second place we get 1.4 beta so the low risk we are giving that return that portfolio is better the second thing we need to understand here in this case is that if you did not correct the calculation of the beta so that means it will have a lot of impact on your calculation so it can jeopardize your ranking thank you