TESLA CAPM

When Analyzing Tesla’s stock relative to the market benchmark using CAPM, we noticed that its ß was 1.72. This means that this stock moves in the same direction as the market, suggesting that Tesla is cyclical. From an objective perspective, we noticed that for every 1 percent move of the market, Tesla would move nearly 2% in the same direction (~1.72%); in other words, Tesla’s stock will move almost twice as much as the market.

+i. While the ß was statistically significant, α was borderline significant with a P-value of 0.08. We would not consider α in this case, which is at 2 percent. +ii. Furthermore, the adjusted R-square was 0.163, which indicates that only roughly 16 percent of the variation of the returns can be explained by the Market (Mf)

CAPM conclusion: given the very low adjusted R-square, we would need to add more variables. For that matter, we will examine the Fama-French approach next.

TSLA Fama-French

2. Fama-French: After running the regression to obtain α and ß, we did not find much improvement in the R-square; it only went up from 0.163 to 0.202. The market ß got reduced slightly to 1.635, reinforcing that Tesla is a cyclical stock. The HML component of the Fama-French model, or the book-to-market ratio, delivered a statistically significant ß of -1.11, indicating an inverse relationship between such ratio and the stock’s return. In other words, Tesla’s stock returns have shown counter-cyclical patterns relative to high (er) book-to-market values. The size factor (SMB) and α were not statistically significant, so they were not considered.

CAPM TOYOTA

1. CAPM: Our analysis suggests that Toyota is also cyclical, given the positive ß at 0.643, which was statistically significant. This means that for every 1 percent change in the market, Toyota’s stock returns will move in the same direction, but its move will be less than 1 percent; in this case, it will be 0.643 percent. The intercept, or α, was not statistically significant and basically zero. The R-squared was 0.269, which suggests that about ~26 percent of Toyota’s stock returns can be explained by the market. It was slightly higher than Tesla.

CAPM conclusion: at only 26 percent of the moves explained by the market, we would explore adding more factors to try and obtain more information to explain such return’s changes.

## 
## Call:
## lm(formula = TM ~ MKT_RF, data = ff_assets)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.133733 -0.024514 -0.000493  0.025256  0.124353 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.001229   0.003944  -0.312    0.756    
## MKT_RF       0.642762   0.088483   7.264 2.03e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04672 on 147 degrees of freedom
## Multiple R-squared:  0.2641, Adjusted R-squared:  0.2591 
## F-statistic: 52.77 on 1 and 147 DF,  p-value: 2.032e-11

TOYOTA Fama-French

2. Fama-French: Adding the factors size and book-to-value ratio added very little value to the model. Our adjusted R-square only moved up to 0.272 from 0.269, basically negligible. Furthermore, the ß for size and book-to-value were statistically insignificant; only the book-to-value was borderline significant with a P-value of 0.0744. We would not consider adding it. This means that neither the market’s size nor the stock price discrepancy are relevant indicators of Toyota’s returns. In other words, the size of the company nor the discrepancy between book and market stock value affect Toyota’s returns

GM CAPM

1. CAPM: General Motors returned the strongest correlation with the market using CAPM. Although its ß was slightly smaller than Tesla’s at ß = 1.447, this also means that aside from moving with the market and being a cyclical stock, General Motors’ returns’ move more than the market. In other words, for every 1 percent change in the market, General Motors’ returns move 1.44 percent in the same direction. General Motor’s ß was statistically significant while α wasn’t, with a P-value of 0.08 (borderline). We would not consider α to be an important indicator.

Conclusion CAPM: Although the adjusted R-squared obtained was larger than in the previous two stocks, it is still worth exploring adding more factors.

## 
## Call:
## lm(formula = GM ~ MKT_RF, data = ff_assets)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.16960 -0.04310 -0.00567  0.03609  0.22757 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.010284   0.005909   -1.74   0.0839 .  
## MKT_RF       1.447679   0.132563   10.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.06999 on 147 degrees of freedom
## Multiple R-squared:  0.4479, Adjusted R-squared:  0.4442 
## F-statistic: 119.3 on 1 and 147 DF,  p-value: < 2.2e-16

GM Fama-French

2. Fama-French: After adding HML and SMB, book-to-value, and size, we found that all ßetas were positive and statistically significant. The positive SMB and HML indicate that General Motors tends to outperform—or experience higher returns—when smaller companies generally outperform larger companies. In other words, General Motors’ returns behave in the opposite way than what Fama-French suggested (small-cap companies outperforming large-cap stocks). Similarly, regarding book-to-value, the ß was positive and suggests that the discrepancy of the stock price also tends to outperform the overall market. The R-squared was 0.53 by adding HML and SMB, which suggests this is a decent model compared to Tesla and Toyota.