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“Everyone in this brief video. We will discuss who or what is responsible for whatever whatever is the performance of a portfolio and we are going to call this performance well an easy way to look at it is to say that the performance of a portfolio could depend on two broad reasons. Let s make a note of these two reasons here well. How we allocate funds over different asset classes could have an impact from how our portfolio is performing.
So let s write down the first reason here asset. Allocation asset location well we may invest some percentage of our funds in equities. Another percentage in let s say debt securities and yet another percentage in risk free assets. So what we are saying is that how we are distributing our funds or allocating our funds to broad asset classes can affect the performance of a portfolio now within each asset class.
We focus on various sectors and then the securities or assets. Within the sector. So we have to select some securities within each asset class. Now and that could be the second reason that could affect the performance of our portfolio.
So we could write it here as security selection. So two reasons here asset allocation and security selection within each asset class. Now since each asset class. Contributes something to portfolio performance.
We need to see how much of this contribution is because of our asset allocation decisions and how much is because of our security selection let us say we have a benchmark for each asset class. So let me write this word here benchmark. Well. What what s a benchmark some some sort of a standard for example s.
P. 500. Index could be a benchmark for equities. Likewise.
Other asset classes would also have benchmarks now let us say. We allocate xb1 proportion of our funds to asset class. One. Where x.
Is the weight and b1. Is the benchmark for asset class. One likewise. We could invest another proportion to asset class.
2. And yet another proportion to let s say asset class..
3. And we could go on depending on how many asset classes. We are contemplating let s also say that the return offered by the benchmark for the first asset class. Is our b1 for this one.
It s our b2 for this one it s our b3 and so on it could be it could go on till our b n. So that if we have a portfolio of benchmarks. What return this portfolio is going to offer us let s write. It as capital r.
And b. For benchmarks. So the return would be for all asset classes. Wearing from 1 to n.
We multiply the proportions xb. I times r b. I so this would be the return offer to us by a portfolio of benchmarks well before we move further we need to ask why we have decided to allocate. What we allocate to each asset class.
For example. If i say i m going to allocate 80. 10. And 10.
Over equity debt and t bills. Well. I need to then provide a justification for this 80. 10.
10. Scheme well somebody could ask me why not 70 2010. Well. The waiting s are going to depend on our clients.
His willingness to take risk if a particular investor for example is very risk averse. I as a portfolio manager in consultation with him or her may decide on a weighting of twenty seventy. Ten distributed over equity bonds and t bills. Respectively.
Now if i decide to deviate from these weightings. I must provide a reason for it otherwise the client is wishing that these should be the weights in which he or she wants to proceed further for his or her investment well let us say i do decide to deviate from the agreed upon weightings..
What will happen then is that i m going to create a new portfolio. Let s say that this portfolio is called portfolio p and like we calculated the return for our benchmark portfolio here we can calculate the return for the new portfolio that i am constructing by deviating from let s say these were the agreed upon weightings for equity bonds and t. Bills. If id be eight from these weightings.
I m creating a new portfolio and the return for that would be let s write it here summation of i wearing from 1 to n. Well something wants to install here on my computer. I ll say later so i wearing from 1 to n. We are taking the sum of let s say x this time xp.
I times rpi. So this is the return on the portfolio that i have constructed now in creating portfolio p. I would have selected some securities. Within each asset class.
Using my own judgment. Or skill or expertise. Call. It.
What you will now if the return on this portfolio. Differs from the return that is offered by the benchmark portfolio. It could only be because of two reasons. Either the reason is that i am using different weights.
I am deviating from the agreed. Upon weighting scheme. So my asset allocation may be making a difference. Asset allocation could be the reason.
I m using different weights. Another reason could be that i have used my own expertise or judgment or skill or maybe. It s just pure luck and because of that the return that is being offered to me here by the individual assets in each asset class. Is different from what is offered by the benchmark well let s say if the s p 500 index is offering me a 5 return per annum by selecting some other stocks i may either outperform.
That benchmark or underperform that benchmark so this return. So. The difference in this return could be another reason. Why my portfolio return is different from the return.
Offered by the benchmark portfolio. So we could write that again as security selection..
So let us say then then the return on the portfolio that i have constructed as a portfolio manager is not equal to what is the return offered by the benchmark portfolio. If i want to write the difference in returns of these two portfolios. I can simply subtract one return from the other let s just write it here formally rp minus rb. We want to find out how much is the difference between returns of these portfolios.
So let s write it here i m just using what we wrote before i m first of all writing the return. Offered by portfolio p. And from that i m subtracting. The return that is offered by the benchmark.
Portfolio xbi times r. Be i right i could take this sum sign outside the bracket so that inside what i have is only the terms xp. I times rp. I minus xb.
I times r be i so this is the difference in returns of the two portfolios well as we said before the difference in returns could either be because of my asset allocation decision. Which is now different from what we agreed upon here or it may be because i have demonstrated some skills. And i have been able to beat the benchmark the security selection or if my skills were poor. Then the returns would be less than the benchmark that would also be attributed then to how i selected the securities.
What i need to do is to separate out these two effects well this is the total difference between the returns of the two portfolios. I want to find out well this difference here the total difference how much of this can be attributed to let s say. Security selection and how much of it can be attributed to asset allocation. That is all that i want to do let me complete this word.
Here. Security selection. Okay let s talk about security selection. First let s say well i m investing this percentage of funds in my portfolio.
Xpi and the difference between the returns of this portfolio from the benchmark portfolio. Maybe because the assets that i have selected within each asset class. Offer me let s say this much return. Which is different from the returns.
That are offered by the benchmark. So this is the effect of security selection. We have just multiplied our portfolio weight by the differential returns. This is the second reason then asset allocation well it could be that the returns of my selected securities is not very different from the benchmark and then what is making the difference.
The only other thing that could make a difference would be how i am distributing my money over different assets so how i allocate my funds across across asset classes in other words. The waiting s that i m using may be making a difference..
We can write this as well the returns are not too different so i m just going to write returns. I m going to use the returns of the benchmark because they are not significantly different from the portfolio returns. What is making the difference is the difference in the weighting scheme. So this is the difference in the weighting scheme.
And because this is for all the securities in all asset classes. Let s not forget the some signs so this thing. This is the attribution to asset allocation. Here you will notice that if we add these two terms this one here and this one here we are going to return to this equation.
We can verify that out very quickly let s do it here well let s add these two terms together let s say the total difference between the returns of my portfolio. And the benchmark portfolio can be written as let s write down this sum sign outside the bracket and inside let us write the contribution made by a security selection xpi times. Well let s multiply out these xpi times rp. I minus xp.
I times r bi and we are adding to this the second term. Which is what let s multiply out these items are bi times. X. Xp.
I minus r bi. Times x. Bi. Let s see now if something can cancel out well we have a minus x bi times rb.
I here and we have a plus x bi times rb. I here so this is going to cancel out with this so what we are going to have here. Now is xp. I times rpi minus this item here x.
Bi. Times r b. I. Which is this item is the same thing as this item here so if we add the contributions made by a security selection and asset allocation decisions we come back to the total difference between the returns of our portfolio and the return offered by the benchmark portfolio.
But we have succeeded now in attributed this total difference to number one security selection. This is the contribution of security selection and number two the contribution made by our asset allocation decisions. Well. This is all i wanted to cover in this brief.
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