31st july 2015

Friday, last day of the month and by so doing would be my cds day. I woke up by 8:30 today, and left by 9. I got there late, with the local government inspector already addressing corp members. I breezed in and was standing because there were no empty seats left. She warned us not to come late again, and being the first general cds, she would forgive us for coming late.

We finished, and she signed our cds cards; i was on my way home after i got my card signed. I had an arrangement that I would go to the bank nysc assigned me to, to collect my atm card, and also to have a haircut. Like i planned to, i collected the card some hours later, then stopped by my barber’s shop to get a haircut. In return I got scars and cuts on my face. It is because of the clipper, I have been told that it needs adjustment, but I have no one to help me with the adjustments; the barber volunteered though after i relayed to him my predicament. He told me he knew someone that could fix it for me, and that I can drop the clipper with him when he his coming around.

On getting home, I read something on investments.

**Investments**

An investment can simply be defined as a current commitment of money for a period of time in order to derive a future payment of sets of payment to compensate the investor for the time and expected rate of inflation during this period and also to compensate for the uncertainty of the future payments.

The main purpose for investing is for an investor to earn a return on his investments. This is the return they aim to get from saving due to their deferred consumption.

**Measure of return and risk**

Historical rates of return

The purpose of investing is to defer current consumption in order to aid our wealth, so that we can consume more in the future. To ensure that we can consume more on a particular investment, when comparing two stocks for example with different prices and returns, we have to take into cognizance the historical rates of return. That means that we have to consider all the changes in wealth, which may be either due to cash inflows such as interests or dividends or caused by a change in the price of the asset. This is so because of liquidity needs, you might need to terminate investments at a particular point in time, and if historical rates are not constant you might lose value in your investments at the time you seek to meet your liquidity needs

The period which an investment is owned is called the holding period, and the return for that period is the holding period return.

The formula for holding period return =

Take for example, you commit $5000 at the beginning of the year and you get back $5500 at the end of the year. The hpr for the year is

Ending value of investment / Beginning value of investment= 5500/5000= 1.10.

The Hpr for the period is 1.10.

The holding period return is great for expressing a change in value of an investment, but investors generally evaluate returns in percentage terms on an annual basis. To convert the Hpr to percentage, we need to subtract the HPR by 1 and then we get the holding period yield.

HPY= HPR-1

To compute an annual rate for the holding period return, we say Hpr^{1/n}

Example : An investment of $400 held for 3 months earned an interest of $50, calculate the hpr and the annual rate of return.

Answer:

Earning at the beginning of the period = $400

Earning at the end of the period= $400 + $50 (Interest) = $450

Hpr = Value at the end of the period / value at the beginning of the period,

Hpr= 450/400= 1.125.

Annual rate is hpr^{1/n}

Where Hpr= Holding period return

N=Number of years.

From the question, the return is earned on the investment after holding it for just 3 months. So n in this case would be 3/12= 0.25.

To reiterate ,Hpr = 1.125

N= 0.25

The annual rate then would be 1.125^{1/0.25 }= 1.5735

**Mean historical return**

What value does the mean historical return have?

In a situation where there are several lows and peaks, like for example a stock. The HPY in a single period might be deceiving; there might be high rates of return or possibly negative rates of return during other periods other that at the beginning period or ending period.

We are to take recognition of all these when making investment decisions. This is where the mean annual rate of return of the holding period yield comes into play. It is a summary figure that indicates the investment’s typical experience or the rate of return you might expect to receive if you owned this investment over an extended period of time.

There are two summary measures of return performance using the mean annual rate of return, the first is the arithmetic mean return and the second is the geometric mean return.

Arithmetic mean= SHPY/ N

Where:

SHPY = Sum of annual holding period yields

N= number of years.

Geometric mean = (Hpr_{1} x Hpr_{2…………….}Hpr_{n}) ^{1/n} – 1

**Expected Rates of return**

Risk is an uncertainty that an investment will earn its expected rate of return. An investor anticipates possible future returns when analyzing an investment. When asked on the spot, the investor might say that his expected rate of return is 15%. This is actually the most likely estimate which is called the point estimate return. He might admit later that under certain conditions, the annual rate of return on the investment might go as low as -12 percent and reach a peak of 30 percent. The specification of a larger range of possible returns from an investment indicates the investor’s uncertainty regarding what the actual return would be. Therefore a larger range of possible returns implies that the investment is riskier.

When analyzing investments, probability comes into play, the investor assigns probability values to all possible returns which ranges from 0 to 1 . 0 means there is no chance of it occurring while 1 means that there is certainty the return must occur.

The formula for expected return =

Expected return = S^{n }(probability of return) X possible return

Take for example the analysis of a market in the next six month based on if it would be bullish or bearish in constant, i.e. no change and the probability and expected returns are as follows:

CONDITION | PROBABILITY | RATE OF RETURN |

Bullish Market | 0.20 | ^{ }0.40 |

Bearish Market | ^{ }0.20 |
-0.10 |

Constant or no change | ^{ }0.40 |
^{ }0.10 |

^{ }

The computation of the expected rate of return is as follows

S (R_{1}) = (0.20*0.40) + (0.20 (-0.10)+ (0.40*0.10)

= 0.08 + (0.02) + 0.04

= 0.10

**Measuring the risk of expected rates of return**

In measuring the risk of an investment, we identify the range of possible returns of an investment and then assign weights based on the probability of occurrence. Then we analyze the dispersion of the expected returns based on the probability of occurrence of possible outcomes from the possible rates of return.

Two common methods of measuring dispersion are the variance and standard deviation.

Variance = S^{n}_{r=1 }(Probability) x (possible return – expected return)^{2}

The larger the variance, the greater the dispersion of expected returns and in so doing, the greater the uncertainty or risk of the investment.

Standard deviation = √variance.

**Recommended Reading **

Frank Fabozzi., Financial management and analysis