Log-Return simulation in R does not lead to expected result -

-

i'm trying simulate log-returns in r , calculate expected p&l simple investment. code working, have problem in understanding why expected profit not equal to:

(exp(annual_mean * (holding_period/253)) * investment) - investment

which equals 5350 in example. however, running following simulation results profit of around 5580:

investment <- 1000000 holding_period <- 45 annual_mean <- 0.03 annual_sd <- 0.05 simulations <- 1000000    # create matrix log-returns   paths <- matrix(data = na, nrow = holding_period, ncol = simulations);     # feed matrix log-returns   (k in 1:simulations)    {   returns <- rnorm(holding_period, mean = annual_mean/253,    sd = annual_sd/sqrt(253));   paths[, k] <- investment * exp(cumsum(returns));   }    # calculate epnl   epnl <- mean(paths[holding_period, ] - investment);   print(epnl)

considering high number of simulations wouldn't expect such big deviation expected profit. tried higher number of simulations result still same.

i'm trying show simulation higher number of simulations closer actual value gets expected value.

i hope guys understand question. know more finance related topic guess there misinterpretation in code side.

thanks lot!

i believe issue use of cumsum - treating returns if rates add rather multiply/compound. if alter code , use cumprod instead, seems give right result...

# feed matrix log-returns (k in 1:simulations)  { returns <- rnorm(holding_period, mean = annual_mean/253, sd = annual_sd/sqrt(253)) returns <- 1 + returns paths[, k] <- investment * cumprod(returns) }  # calculate epnl epnl <- mean(paths[holding_period, ] - investment) print(epnl)

Comments

Post a Comment

Popular posts from this blog

ios - RestKit 0.20 — CoreData: error: Failed to call designated initializer on NSManagedObject class (again) -

-
this error has shown on many times, seems. prominent answer issue seems restkit 0.20 — coredata: error: failed call designated initializer on nsmanagedobject class however, solution posted doesn't work me. let's start beginning: i want upload file server. want parse response make sure uploaded. if not, try again later. model has boolean variable called nsnumber *senttoserver purpose (in coredata, bool saved nsnumber ) . because don't know whether sending going successful, save entity coredata model first before sending via restkit. when post request successful, server returns json string this: {"id":14,"created":true} notice that, of course, id not set on coredata model yet, both id , created new informations model. here's model: @interface recording : nsmanagedobject @property (nonatomic, retain) nsstring * audiofilepath; @property (nonatomic, retain) nsdate * createdat; @property (nonatomic, retain) nsstring * deviceid; @...
Read more

java - Digest auth with Spring Security using javaconfig -

-
so i'm trying create digest authentication spring following documentation trying translate xml "requirements" in java requirements. let's have xml in docs: <bean id="digestfilter" class= "org.springframework.security.web.authentication.www.digestauthenticationfilter"> <property name="userdetailsservice" ref="jdbcdaoimpl"/> <property name="authenticationentrypoint" ref="digestentrypoint"/> <property name="usercache" ref="usercache"/> </bean> <bean id="digestentrypoint" class= "org.springframework.security.web.authentication.www.digestauthenticationentrypoint"> <property name="realmname" value="contacts realm via digest authentication"/> <property name="key" value="acegi"/> <property name="noncevalidityseconds" value="10"/> </b...
Read more

laravel - PDOException in Connector.php line 55: SQLSTATE[HY000] [1045] Access denied for user 'root'@'localhost' (using password: YES) -

-
my .env: app_env=local app_debug=true app_key=myappkey app_url=http://localhost db_connection=mysql db_host=localhost db_port=3306 db_database=gestiontaller db_username=root db_password='root' cache_driver=file session_driver=file queue_driver=sync redis_host=127.0.0.1 redis_password=null redis_port=6379 mail_driver=smtp mail_host=mailtrap.io mail_port=2525 mail_username=null mail_password=null mail_encryption=null i've tried password ", ' , without, restarting server every time. i've tried changing localhost 172.0.0.1. yes, password correct, running mysql -u root -p introducing password root in prompt can go mysql. users table: +------------------+-----------+ | user | host | +------------------+-----------+ | debian-sys-maint | localhost | | mysql.sys | localhost | | root | localhost | | root1 | localhost | +------------------+-----------+ i've added homestead.yaml this: database_port: 3306 ...
Read more