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# System prepended metadata

title: '張鴻文:投資貝萊德股票(BLK)或iShares Core S&P 500 ETF (IVV)'

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# 張鴻文:投資貝萊德股票(BLK)或iShares Core S&P 500 ETF (IVV)

## 1. 動機 :
動機 : 錢要投資基金公司股票?或投資基金?何者績效較佳?

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![](https://i.imgur.com/0rEbKxd.jpg)

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## 2. 資料視覺化 :
1.BLK表現 : 股價呈上漲趨勢

![](https://i.imgur.com/VCRczgz.png)

![](https://i.imgur.com/RRDFUf4.png)

策略 : 長期投資

![](https://i.imgur.com/TmmgF9T.png)

股利成長

![](https://i.imgur.com/KAlKSTC.png)

美股股利採季配息

### Data

| Date      | Dividend | Price  |Dividend Yield|
| --------- | -------- | ------ | --------- |
| 2016/12/8 | 2.29     | 390.33 | 0.5867    |
| 2017/3/2  | 2.5      | 391.65 | 0.6383    |
| 2017/6/1  | 2.5      | 413.38 | 0.6048    |
| 2017/8/31 | 2.5      | 419.01 | 0.5966    |
| 2017/12/1 | 2.5      | 502.08 | 0.4979    |
| 2018/3/6  | 2.88     | 548.66 | 0.5249    |
| 2018/6/6  | 2.88     | 551.86 | 0.5219    |
| 2018/9/6  | 3.13     | 471.96 | 0.6632    |
| 2018/12/6 | 3.13     | 400.23 | 0.7821    |
| 2019/3/5  | 3.3      | 432.52 | 0.7630    |
| 2019/6/5  | 3.3      | 438.15 | 0.7532    |
| 2019/9/4  | 3.3      | 415.64 | 0.7940    |
| 2019/12/5 | 3.3      | 490.3  | 0.6731    |
| 2020/3/4  | 3.63     | 495.31 | 0.7329    |
| 2020/6/4  | 3.63     | 546.19 | 0.6646    |
| 2020/9/3  | 3.63     | 579.12 | 0.6268    |
| 2020/12/3 | 3.63     | 715.42 | 0.5074    |
| 2021/3/4  | 4.13     | 683.21 | 0.6045    |
| 2021/6/3  | 4.13     | 881.01 | 0.4688    |
| 2021/9/3  | 4.13     | 937.28 | 0.4406    |

![](https://i.imgur.com/OFOIPCM.png)


2.IVV表現 : 股價呈上漲趨勢

![](https://i.imgur.com/2CiGOUq.png)

![](https://i.imgur.com/aVJMT8Z.png)

策略 : 長期投資

![](https://i.imgur.com/ODQZJek.png)

配息穩定

![](https://i.imgur.com/6DYYttM.png)

偏差值係多配一次息所致

| Date    | Dividend | Price  | Dividend Yield |
| ---------- | -------- | ------ | ------------|
| 2016/12/21 | 1.304    | 226.85 | 0.5748      |
| 2017/3/24  | 1.032    | 235.39 | 0.4384      |
| 2017/6/27  | 1.117    | 243.03 | 0.4596      |
| 2017/9/26  | 1.284    | 250.75 | 0.5121      |
| 2017/12/19 | 1.273    | 269.13 | 0.4730      |
| 2018/3/22  | 1.229    | 265.47 | 0.4630      |
| 2018/6/26  | 1.281    | 273.47 | 0.4684      |
| 2018/9/26  | 1.277    | 292.02 | 0.4373      |
| 2018/12/17 | 1.442    | 255.65 | 0.5641      |
| 2018/12/28 | 0.322    | 249.33 | 0.1291      |
| 2019/3/20  | 1.13     | 283.39 | 0.3987      |
| 2019/6/17  | 1.778    | 289.74 | 0.6137      |
| 2019/9/24  | 1.483    | 297.51 | 0.4985      |
| 2019/12/16 | 2.039    | 319.32 | 0.6385      |
| 2020/3/25  | 1.531    | 247.47 | 0.6187      |
| 2020/6/15  | 1.261    | 306.89 | 0.4109      |
| 2020/9/23  | 1.506    | 323.75 | 0.4652      |
| 2020/12/14 | 1.61     | 364.35 | 0.4419      |
| 2021/3/25  | 1.311    | 391.12 | 0.3352      |
| 2021/6/10  | 1.225    | 424.04 | 0.2889      |
| 2021/9/24  | 1.693    | 445.74 | 0.3798      |

![](https://i.imgur.com/idb2KkA.png)


### 統計量
|Numerical Measures|Value (BLK)|Value (IVV)|
|:----|-----|-----|
|Mean|0.6233|0.4576|
|Median|0.6158|0.4630|
|Range|0.3533|0.5094|
|Standard Deviation|0.10705|0.11773|
|Variance|0.01146|0.01386|
|Q1|0.5219|0.4109|
|Q3|0.6731|0.5121|
|IQR|0.1512|0.1021|


## 3. 問題重建與統計分析 :

#### Problem formulation 1/2
1.令隨機變數$X$為BLK的年化殖利率(單位為百分比 %)，假設殖利率服從常態分配 $X_i \sim N(\mu_i, \sigma_i^2)$。 
2.令隨機變數$Y$為IVV的年化殖利率(單位為百分比 %)，假設殖利率服從常態分配 $X_j \sim N(\mu_j, \sigma_j^2)$。

#### Problem formulation 2/2
2016/11~2021/10買BLK的平均殖利率$\mu_i$，IVV的平均殖利率$\mu_j$，我們想知道$\mu_i$ < $\mu_j$ 
#### Statistical analysis 
1. 建立虛無假設
$$\begin{cases}H_0: \mu_i-\mu_j\leq 0\\
H_1: \mu_i-\mu_j> 0\end{cases}$$
2. 給定顯著水準$\alpha=0.05$。
3. 檢定統計量$t_{stat}=\frac{(\bar{X_i}-\bar{X_j})-D_0}{se(\bar{X_i}-\bar{X_j})}\sim t_{(n_i+n_j-2)}$
4. 找出拒絕域: $\{t>t_{(n_i+n_j-2,\alpha)}\}$，其中門檻值為 $t_{(n_i+n_j-2,\alpha)}=1.685$
5. 資料算出的實現檢定統計量: $t^\ast=\frac{0.6233-0.4576}{\sqrt{0.01269(\frac{1}{20}+\frac{1}{21})}}=4.7077$
6. 因為實現統計量落在拒絕域，我們拒絕虛無假設!

## 4. 結論 :
1. 貝萊德股票(BLK)的殖利率看起來是大於iShares Core S&P 500 ETF (IVV)的殖利率。
2. 延伸不負責任之量化投資建議: 可以考慮長期持有基金公司貝萊德股票(BLK)，取代基金公司的基金iShares Core S&P 500 ETF (IVV)!


## 5. 資料存放 :

| No | File | Description  |
|---|---|----|
|1|[BLK](https://docs.google.com/spreadsheets/d/1HCuVvBPS48ALw75BBxyBLkG4CttlPVlZ/edit#gid=634777677)|股價|
|2|[BLK](https://docs.google.com/spreadsheets/d/1BDFeaLl2ikVp6_N3V4rKqUG1RBChGKiS/edit#gid=1237226202)|股利|
|3|[IVV](https://docs.google.com/spreadsheets/d/1C5ubMuZ5jeFcutj5ugRkVMbfdBEkEZ0P/edit#gid=2146630243)|股價|
|4|[IVV](https://docs.google.com/spreadsheets/d/12Y5CRhArTOON3TEY-AJTiM88kuANk4Cr/edit#gid=1821952328)|股利|










