Why Analysts’ Valuation Does Not Apply To Retail Investors?

Not many retail investors do their own valuation analysis when investing in the stock market.  Some rely on news, technical analysis or analyst’s report.  In many analysts’ reports, especially those who use discounted cash flow method or dividend discount model (DDM), the stock value is estimated based on certain assumptions, which may not be applicable to retail investors.

One of the key factors in valuation is the required rate of return, k.  It is inversely proportional to the value of the stock.  There are few methods to estimate k, the most common one is Capital Asset Pricing Model (CAPM).

The formula for CAPM is

where,

k = required rate of return

R_f = Risk Free Rate

β = Beta

R_m = Market Return

R_f and R_m are the invariant to all investors.  The factor that differentiate analyst and retail investor is the β.  Beta (“β”) is a measure of the risk arising from exposure to general market movements as opposed to idiosyncratic factors.  β is measured through the eyes of the marginal investor in equity (rather than the retail investor). The marginal investor is an investor who owns a well-diversified portfolio and trades frequently, for example, a Fund Manager.

If you are a retail investor who does not hold a well-diversified portfolio, the beta has to be adjusted to reflect your risk.  Aswath Damodaran, the valuation guru from NYU Stern Business School, stated that “total beta” is more appropriate for the average investor (Read more here).   The “total beta” is derived by dividing the beta with the correlation coefficient of the stock and the market portfolio.

The mathematics involved in calculating “total beta” may be discouraging, so what could a retail investor do in order to correctly adjust for the risk?  Since the correlation coefficient is always less than 1, which means the “total beta” will be always higher than beta.

As such, the required rate of return, k, is relatively higher for a retail investor.  This means that the value of the stock from the eyes of retail investor shall always be lower than the number reported by an analyst!

Moving Average as Momentum Indicator

Moving Average (MA) is a very popular indicator to gauge the trend of stock market.  Conventionally, 200-days MA is the barometer of portfolio managers to rebalance their position.    This week, we are going to demonstrate another usage of MA, as a momentum indicator.

In a previous article, we demonstrated the usage of Fourier Transform to determine the market cycle of KLCI (Read more here).  From a medium-term perspective, 61 days is a significant market cycle.  As such, a 61-day simple moving average is plotted on top of KLCI data in the following chart.  The black curve is the daily closing price of KLCI while the blue curve is the 61-day MA.

The Over Sold indicator is computed by studying the gap between 61-day MA and daily closing price.  If the immediate gap is larger than 70% of the normalized gap over the observation period, it will be classified as Over Sold, which is plotted as red in the chart.  The Over Sold indicator did detect several reversal points over the observed period.

Fourier Transform to Determine Market Cycles

Fourier Transform is one of the most important tools in the modern signal processing world.  It is widely used in communications, geology, acoustic and engineering field.  However, its capability to decompose time series data into frequency domain has extended its usage to other fields such as finance and business (Read more here).

In finance, moving average is a common indicator to track the movement of the stock market.  However, the period of the moving average indicator is normally selected at the discretion of the users, which sometimes may not be appropriate.  Fourier Transform is a good tool to determine the period for the moving average.  The following graph shows the significant period of the KLCI daily closing price determined by Fourier Transform.

From the graph, short term significant periods are 8 and 17 days while medium term significant periods are 28, 43, and 61 days.  Fourier Transform computations could be found in popular engineering software such as MATLAB or Excel Analysis ToolPak (Read more here).

“Recession” or “Rebound”?

In a previous article, stock market movement prediction using Google Trend search term (Read more here) was demonstrated.  This week, a new search term will be used to study the stock market direction.

In the following graph, the search term “Recession” frequency and the MSCI World Index were plotted together from 2004 to 2018.  The frequency of the search term is plotted in orange while the blue curve is the MSCI World Equity Index.

Coincidently, two significant peaks of the search term frequency (red circle) occurred at the reversal of the market down trend.  This suggests that market might rebound when the sentiment is very negative.  So, our next question is whether the current “recession” sentiment has reached its peak?  Google Trend might have the answer perhaps?

Asset Class Performance in 2018

Wondering you have chosen the correct investment in 2018?  The following graph shows the various asset class performance in 2018.  2017 market’s darlings such as cryptocurrency and oil were the biggest losers in 2018.  Bitcoin and Oil dropped more than 70% and 25% in 2018 respectively.  Hang Seng dropped 14% while S&P500 and KLCI dropped 6.2% and 5.9% respectively.  Gold lovers were not amused with their collection as their return was at negative 1.7%.  The safe haven was fixed deposit which yielded 3.5%.

In a previous article on P2P lending investment (Read more here), we featured the return could be at an average of 10%.  The author has experimentally invested in the P2P platform and gained 12.59% in 2018.  This shows that it is always good to diversify your portfolio in some alternative investments.

If you are interested to invest in P2P lending, you could sign up using the following link

https://fundingsocieties.com.my/sign-up-investor?referral=jakdytp6

Disclosure: The author will receive a one-time referral fee of RM50 for each new investor who signs-up via the above link AND invest at least RM1,000 (Read more here).

Probit vs Logit

On 19 December 2018, S&P500 dropped 1.54%, the next day (20 December 2018), KLCI dropped 0.31%.  The linear and logit regression model published on 14 December 2018 (Read more here) predicted the KLCI would fall 0.37% and the chances of the drop are as high as 75%.  This shows that the quantitative approach is indeed decent. 

Besides logit model, one could also use a probit model to run similar analysis.  In the logit model the log odds of the outcome is modelled as a linear combination of the predictor variables.  Meanwhile, in the probit model, the inverse standard normal distribution of the probability is modelled as a linear combination of the predictors.

Chart 1 shows the probability plot for both logit and probit models.  Both models should give similar results.  The slight difference is logit model has fatter tail.

Chart 1

Table 1 is the summary of the probit regression with the estimated coefficients.  The p-values show that the slope is significant but the intercept is not significant.  However, the impact of the intercept to the estimated probability is about 0.5%, which is relatively small, and also the condition where X = 0 is not modelled in this setup.

Table 1

Logit Regression on Overnight S&P500 Performance Impact on KLCI

We often hear that overnight US stocks performance might have an impact on KLCI the next day.  But how shall we quantify this?  A simple linear regression could be used to estimate the KLCI performance based on overnight Wall Street results.  However, the goodness-of-fit is usually poor. 

Chart 1 and Table 1 shows the regression plot and ANOVA table for overnight S&P500 and next day’s KLCI index performance using daily closing data from November 2015 to December 2018.  The R² is low at 0.1237.  Nevertheless, the significant of the slope’s p-value suggests that there are positive correlation between S&P500 and KLCI.

Chart 1 

  

Table 1

Let’s ask the next question – what is the probability of the KLCI to close positively or negatively, given the performance of overnight S&P500?  To answer the question, we could use logistic regression (“logit”) to study the probability.  Logistic regression is used in various fields, including machine learning (Read more here).  It uses a logistic function to model a binary dependent variable.  The logistic function is constructed based on linear regression model.

Linear regression model is

In logit model, Y value is labelled as “1” if KLCI gain on the next day or labelled as “0” if KLCI loss on the next day.  X is the overnight S&P500 performance while b₀ and b₁ are the coefficients.

The probability of the function with given X value is

The coefficients are then estimated using Maximum Likelihood Estimation (MLE)

Table 2 shows the first 5 rows of the data and their respective equations while Table 3 is the summary of the logistic regression with the estimated coefficients.  The p-values show that the slope is significant but the intercept is not significant.  However, the impact of the intercept to the estimated probability is about 0.5%, which is relatively small, and also the condition where X = 0 is not modeled in this setup.

Table 2

Table 3

 

Now back to our question, what is the probability of the KLCI to close positively or negatively, given the performance of overnight S&P500?  Chart 2 is the probability of KLCI Gain/Loss on next day given overnight S&P500 performance.  The probability distribution shows that if overnight S&P500 gained 5%, it is almost 99% sure that KLCI will gain on the following day.  If overnight S&P500 gained 1%, the chance for KLCI to gain on the next day is around 70%.  What if overnight S&P500 loss 2%?  Then the probability of KLCI to close positively on the following day would be around 15%.

Chart 2