Hello, and welcome to this bonus lecture. There are a lot of investment options available in this world. However, not all investment options are suitable for everyone. A person must very carefully determine what is his or her risk appetite. And then based on his or her risk appetite, the person must select which investment option he or she would like to invest in. In this lecture, we discuss a mathematical treaties of how to use risk appetite to determine the investment option.

Before we discuss risk appetite, let us discuss what are the different investment choices available to us. The investment choices mentioned here are no means an exhaustive list. However, these are the most commonly used investment options investment choices are listed below in the increasing order of the risk, the least risky is considered to be the government bonds, then we have corporate bonds or municipal bonds, then we have fixed deposits or recurring deposits. A more risky option is insurance. Then we have mutual funds which are considered more risky and then we have the shares, which are very risky. government bonds are also known as treasury bills in many countries, there are various types of these, there are boards like infrastructure bonds etc.

National Savings certificate kisaan Casper tra, provident fund can also be considered as government bonds, though these are fixed return instruments. In comparison to government bonds, provident fund can be considered more risky as the rates are vary by the government from time to time. There are various types of corporate bonds or municipal bonds. Normally, the riskiness of the corporate bonds is determined by the rating like triple A is less risky and double B is more risky etc. There are various types of deposits or recurring deposits also fixed deposits or recurring deposits issued by public sector banks, by private sector banks by cooperative banks, Cooperative Bank fixed deposits are more risky as compared to public sector fixed deposits. Among insurance also we have various options.

These options are listed here in the increasing order of the riskiness activities are normally very less risky. Then we have conventional insurance, usually click insurance are normally very high risk about mutual funds. Also we have various options. Like we have debt funds which are less risky. We have balanced bonds which are balanced between debt and equities, then we have equity parts, which are more risky. the share market is considered to be the riskiest of most of the options, but there are options which are more risky than share market as well.

Other instruments of investments are investment in gold, investment in real estate, investment in hedge funds, etc. Any investor should create a diversified portfolio, which means that the investments of investor should be in many of these instruments that are listed here. Never the investor should invest only in one instrument. Any investor considers various parameters before making an investment The preferred investment instrument depends on the risk appetite of the investor. So, we will study about this can be tied in this lecture. This capital appetite defines the investors attitude towards risk the investor can be risk averse that means, the investor does not like to take any risks or the investor can be this neutral that is the investor takes risk on certain circumstances and does not take risk in other circumstances or they can be investors who are risk takers who basically look for risky instruments to make higher amount of profit.

One measure of risk in the investment world is variance or standard deviation standard deviation is basically the square root of variance. So, greater variance, we consider the investment instrument to be more risky. Like I mentioned before, government bonds are considered to be zero risk or risk free. So, if you invest in government bonds, you should be assured of getting your returns back. Now, less the risk means less will be the returns from the investment instrument. In practical terms, fixed deposits from big banks can be considered as this free though this may not be the case in modern world in Europe today.

Now, mathematically risk free means that standard deviation is equal to zero for the investment instrument has it example, let us consider how to calculate the standard deviation for a mutual fund. Supposing we have a mutual fund, which gives the following returns in the months, we first find the mean of this return. So the mean can be found by adding all the returns and dividing by total number of returns that is equal to nine. So, we get a mean of 13.1956%. So, this should be the expected return from this mutual fund. Next, let's calculate the variance.

To calculate the variance, we take each return and subtract the mean and square it. These square terms we add them up and divide by n minus one. So, that is nine minus one or eight So, we get a variance of point 4459 percent the standard deviation can be kept computed by taking the square root of the variance. So, we get 6.6776% as the standard deviation of the mutual fund for the return stated here. Now, we come to the big question every investor has, is there a scientific way to determine which instruments to invest in? Fortunately, the answer is yes, there is a scientific way by which we can decide which instruments is suitable for a particular investor.

We can determine which investment instrument is suitable for the investor by finding the utility of the investment for the investor. Now, utility is an economic term and it can be defined mathematically In economics, we define utility as the sense of pleasure or satisfaction that comes from consumption. So, in terms of investments, the utility means that the sense of pleasure or satisfaction that comes from getting returns from our investment, the utility derived from a particular good or service or activity depends on the consumers taste or preference. Mathematically, utility can be defined as utility is equal to expected returns minus half of coefficient of risk aversion into variance. So, we can write it as utility is equal to E r, e r representing expected returns minus half of a star So this coefficient of risk aversion into sigma squared, sigma is the standard deviation. coefficient of risk aversion a is defined as follows.

The person who says to Me discovers if the coefficient of risk aversion is greater than zero, so higher the number for a greater than zero, the person is more risk averse. A person who said to me this neutral coefficient of risk aversion A is equal to zero. This fakers have a coefficient of risk aversion which is less than zero. So smaller the number less than zero, the person is a bigger risk seeker. To understand how to determine the investment instrument suitable for a person, let's consider an example. So an investment option one might investor invests in fixed deposits at six 7.10% per annum.

So, in this case, the expected return is 7.10% per annum and the variance is equal to zero. We also consider investment option two in which the investor invest in a mutual fund. Now, we assume that that mutual fund will return 50% at 70% probability at minus 20% or 30% probability. So, in this case the expected return is determined by multiplying the probability with the return and adding them up. So, we get 29% the variance of this particular investment can be 10.29%. So, now the question is which investment option is better?

We will soon find out that whether the investment option is good or bad depends on the investor We first consider the case of a risk neutral investor. So, for this investor a, the coefficient of risk aversion is equal to zero. Let's calculate the utility for the investor. So, you can see the calculation for option one investment option one is 7.10%. And for investment option two, it is 29%. So, clearly for the risk neutral investor, the utility from the option to or investing in mutual fund is mode.

So, the investor should possibly invest in the mutual fund rather than the fixed deposit. Next, let's consider the case of risk averse person. And suppose, the coefficient of risk aversion is equal to three. So, in this case, from investment option one in fixed deposits, the utility is 70 point one zero percent and from investment option two that is mutual fund, the utility is 13.565%. So, clearly for this this investor also the mutual fund has got more utility. Next, let's consider another risk averse person who has a risk aversion coefficient of five.

So in this case, from the utility from the fixed deposit is 7.10%. And the utility from mutual fund is 3.275%. So, clearly for this person, the fixed deposit has more utility and so this person must invest in the fixed deposit. So, from this illustrations I hope you're able to determine how to utilize utility to do Determine which is the most suitable investment instrument for particular investor. Thank you for listening